I'm not gonna lie, this is a bit of an awkward video, but look, where's the direct, right? That's what a lot of people are thinking right now. Where is this Nintendo Direct? Where is the Shadow Drop Nintendo Direct? Where is this partner showcase or a general or a mini? What is going on? We're two weeks into February. Nintendo hasn't given us the goods. So even Nintendo's breaking their own pattern. We have obviously the rumors out there from some trusted insiders. What is happening? What are we doing? Well, I do think that we need to address some of this stuff and also address things I've learned through this process and things I will be changing in the future. But we're gonna get to that. That's gonna be the second half of the video. The first half is gonna actually address well, was there supposed to be a Direct and now it's gone? Well, we have some new information. And again, this is a rumor and you're already gonna see some of the changes in the title and the thumbnail that we're gonna be making in the future just to make sure there is absolutely no confusion. But it's a rumor and it comes from Jeff Grubb. Now, I have reached out to Jeff Grubb privately to just have a small conversation about this rumor. I wanted to see how confident he is and all of this stuff. And based on what he told me about the source, it is a very confident rumor from him. But again, still a rumor. I guess we'll see if it happens next week. Nintendo will probably never confirm this rumor, by the way. But it's neither here nor there. Maybe today's Xbox show at 2 p.m. central time might have been why the Nintendo Direct did not happen today. Let's get into what Jeff Grubb had to say. So over on Twitter, he responded to this guy named Deathbringer who said, what's going on with the Direct? Post phone, canceled, saving for Switch 2 reveal. Here's what he said, I know no one wants to hear this, but this is just like when the Queen died. This is real. I heard earlier this week that they were discussing moving the Direct because of the Xbox business update. I've never known the date for sure. I only ever heard by the middle of February. And then he says, you may now shoot the messenger. So he's taken any bullets that people want to throw his way because of this. I also said this on the last of the Nintendo Dogs on Tuesday, which I went back and listened to. I can confirm he did bring this up on the last of the Nintendo Dogs. But as you know, for some reason, this tidbit didn't do the rounds and get headlines, which it probably should have. And it would make today's video look even better on my end because it would show that, hey, we're hearing something about this before we even got to the 15th. So here we are today, and there is no Nintendo Direct, whether it's a general, a mini, partner showcase. Is it gonna happen this week? Is it gonna happen at all? Are they still gonna announce a Switch 2 in March? That's a lot of stuff that we need to talk about because the two primary sources on this were obviously Necrofilipa Lima from Universal Nintendo, someone we've brought up in the past who said a direct was gonna happen this week on the 15th.  And then just in some other places, like FAMI boards and Reset Era and Twitter and stuff like that, essentially said that he had heard it was going to be this week as well. Now, Nate the Hate for the most part has been pretty silent most of this week. So if he had heard any updates on this, he certainly didn't convey it publicly. The only person to convey a potential update on this was Jeff Grubb. And again, for some reason, it just kind of got ignored. And I take some responsibility for that. I know that I should probably be a regular viewer of the last of the Nintendo just in case Jeff Grubb happens to have a little scoop like that, especially around this Nintendo Direct rumor season. So that is the current update. Whether you wanna believe it or not, it's totally fine. If you wanna go ahead down in the comments and give me flak, I totally understand it because one of the biggest things that we're gonna hear today, at least I'm gonna hear, and I've been hearing it already on social media, such as Twitter, is I lied to everyone and I misled people and I knew what I was doing and I intentionally made people think there was a Direct today and I didn't clarify it was rumors and all of this stuff, which I of course did clarify it was rumors. But when you drop a thumbnail like this that literally just says 2, 15, 20, 24, obviously the thumbnail alone is gonna make people start to believe that it is happening on the 15th. There's also something that I need to remember and this is a lesson I probably should have learned before but honestly, this being one of the really, really big times that some insiders got things potentially wrong, one thing I need to realize in doing this sort of coverage is there's also not just whether or not I believe or don't believe a rumor, that's all gonna be personal opinions. Rumors are always meant to be doubted. I've shown and said that several times. I also need to recognize that there is a level of trust between the audience and me. There are some of you guys that really do trust me and if I start to feel like something is going to happen, you're going to also start to think it's going to happen and because of that, there's a little bit of a responsibility on me to make sure that I am very, very clear on what my opinions are and how I feel about something versus what the reality of that something is and unfortunately, even though I've been putting rumor in my titles, rumor has been in brackets at the end of the title so some people didn't see that. Rumor is also like not in the thumbnail so because of that, there's not direct upfront in your face clarity that what we're about to talk about is meant to be doubted and then obviously separating out here's the rumor and then here's my thoughts and I've been trying to do a better job of separating out this is the news and then this is what I think about the news, trying to take some notes from Philip DeFranco and how he approaches it where he gives the news and then gives his opinion but I just want to make sure that I am more transparent about that moving forward. Transparency is something I talked about a lot in my live streams, how I'm a pretty open book, you can ask me anything, I'll address any criticism, whether you like my response or not, I don't know, I'm admittedly a pretty stubborn person but I do want to learn from situations like this and part of that learning is making sure that as transparent as I might be when you chat with me, I want to be transparent through and through. So a couple changes that I already mentioned earlier, we are for any sort of rumor video, we are going to put the word rumor in the thumbnail. All right, so if we're covering a rumor, I'm actually going to separate that rumor out, it's not going to be attached to other news, okay? We're going to do away with that. Rumors are going to be their own videos and they're going to say rumor in the thumbnail and we're going to put rumor at the very beginning of the title, all right? That's just something that I think is just adding further transparency. I also feel like we should put a disclaimer pinned comment or in the description, maybe two, maybe both, where we note what a rumor means, what the term rumor means, because I think a lot of people go, well, do you believe this rumor? I'm like, well, rumors are supposed to have doubt but just because I might think something's true, I'm also a Nintendo fan. So putting a disclaimer in the description putting the disclaimer down in the comments where it identifies this is what rumor means, so everyone's on the same page, then also trying to remind everyone that I am a little biased when it comes to Nintendo stuff and I have a lot of hopeium and because I have a lot of hopeium if it's something I really want to happen, I might start to get really excited about something that may not happen. I personally don't get that disappointed when things don't happen. Like when a Nintendo Direct wasn't announced this week and then didn't get Shadow Drop today and who knows, maybe it's Shadow Drop later today but as far as we know, isn't being Shadow Drop today, I don't actually get upset about it. As much as the hyping irresponsibly I do, I guess you can argue I'm a mix of hyping irresponsibly with a responsible notion in the back of my head. Like I get really excited for a possibility but I have this acceptance underneath it that it might not happen and I'm not gonna be that disappointed. Like a Direct not happening this week isn't some life altering event for me, right? It's really not that big of a deal. Now, besides being more transparent with my titles and my thumbnails, we also need to be better about who we're covering when it comes to rumors. I know that I have a reputation online. I'm not unaware of this fact that people think I will just cover any old rumor no matter where it's from, whether it's 4chan or Zippo or just some random person, Tommy Bear knows, right? And I'm not gonna lie, it's not like it's a reputation I haven't earned in some respects because in the past, even as early as like, even as like latest as like the beginning of February, I did do stuff like that. And I started feeling really bad about it a few weeks ago and then it's really just come full circle now after some realizations today. So I wanna make sure that if I bring you rumors that it comes from a trustworthy place that is easily sourceable and comes from a place that has a track record. Like when I brought up Jeff Grubb today in this particular video, you guys know who Jeff Grubb is. You know, if you don't know, he works at Giant Bomb. He's worked at other outlets. He's been a video game journalist for a long time. He gets some stuff right. He gets some stuff wrong, but he's more right than wrong. A lot of you will just remember the wrongs because it's really easy to remember that we all wanted Twilight Princess and Windbreaker HD and we all wanted Metroid Prime Remastered to come out in 2022 instead of Shadow Drop to the February Direct of 2023. We all know that stuff. Like keeping track of what he did wrong. The wrong stuff always sticks in our mind. Then we forget about all the times he's been right. He's been right about a number of games that are gonna be indirect. He's been right about direct timing. He's been right about things like the Queen, right? He was the one who broke the story that the Nintendo Direct was about to be delayed because the Queen died. That was not just him speculating. He said he had a source on it. And then literally later that day, Nintendo made an announcement that they were delaying the Direct they had just announced because of the death of the Queen. So that is something that I wanna make sure that I'm just focusing more on the reliable places. I'm not gonna stop talking about rumors as much as many of you might want me to but I do need to be more responsible with who we're covering. So I always threw up like the rumor believability scale. You guys have seen this before, one last look at it. I think I'm gonna toss this in the trash because the rumor believability scale really only needs to exist if I'm covering people that aren't very reliable. If you're covering really unreliable people then you need to start clarifying who to believe. In the end, you shouldn't believe any of them. To be clear, I don't care if it's Pioro with his 100% track record on Twitter. I don't care if it's Jeff Grubb. I don't care if it's Nate DeHeat. I don't care if it is, I don't know. Let's say Reggie Fisame, right? If it doesn't come directly from Nintendo should always have some doubt on whether or not it's true. And if you don't have any doubt I need to do a better job of making sure that you have some. I need to provide arguments for both ways. Both why I really want this to be true and might believe it's true but also provide the opposing viewpoint as well. That way it's a more well-rounded situation. So that is something I wanna do in the future as well. Now, a big reason that someone this comes up is I wanna note who we're not gonna be covering anymore, right? I already talked about how we're not gonna be covering Zippo anymore. We don't, Tommy Bear knows was totally fake. We're not, when we don't really cover 4chan unless it's that unique Pokemon situation like last year where a 4chan post went out and then like months later it turned out almost everything was correct. That's obviously an in hindsight cover. But what I wanna tell you about is I made a mistake and we all make mistakes. And I need to own up to this mistake. I did a lot of deep thought on this today and even yesterday just in case this was coming about why I trust the sources that I do. For the most part, it's because they have a track record, right? Nathan Haidt has a track record that we can check and verify that he's gotten a bunch of stuff right. Yes, he's gotten some stuff wrong, but he's gotten a lot of stuff right. Same with Jeff Grubb, same with Andy Robinson, same with Tom Warren, same with the guys at Digital Foundry. There's a lot of people we can go like, they've gotten a lot of stuff right. Have they been wrong sometimes? Yes, but we can actually look at that track record. One thing I have a hard time looking at are track records of people that aren't English speakers. Trusting leakers that are not in a language that I understand. And that is because it is very hard for me to verify their track records because again, they're in a foreign language. I don't really understand it. I'm relying on Google Translate. It's really, really difficult to dig through everything. And I made a mistake in reporting on a guy known as Necrophilipe Lima. And my mistake, I don't think is that I reported. My mistake is that I kept calling him a person who had gotten a number of things correct in the past. And I called him somebody who was trustworthy. I built trust in him from my audience. And to be clear, I don't know him. I don't know him at all.  Universal Nintendo seems like a pretty neat website. But my trust base in him came from my trust base in FAMI boards. And that was a mistake. It was a mistake, not that I covered him, but that I, well, actually it was just all a mistake. Let's just be honest.  I don't want anyone going to say anything to him. I don't know anything.  I just can't confirm any of it. I can't track his record. I don't, this is a mistake on my end. So I'm no longer going to be covering him. Just like I don't cover Zippo anymore because Zippo has a track record and it's very bad. And I can track that and it looks bad. I want to make sure I'm only covering people that I can actually verify that they are correct most of the time. And that is a change I want to make moving forward. This is going to make rumor videos in the future. I don't want to say more reliable because rumors are meant to be doubted, but they're at least going to make them more fun to talk about because it's going to be a more serious conversation because there's a higher likelihood that the rumor might actually be correct. Again, not believable, but there's a better chance of something Nate that hates us being true than someone who I can't really track anything. And I made this mistake and I deeply apologize to my audience about that mistake. Now, more than this, we need to talk about a couple of the things. One of them is when I get my own sources and I tell you guys, I don't feel like I've made any mistakes in terms of giving you directly what my source is telling me when they give me permission to do so and the trust I build in some of the sources I have and the credibility they have for me behind the scenes. But I do need to be, again, this is one of those things with rumors, careful to make sure I clarify, this is what the actual information is and this is my opinions and thoughts on that information. I am in the past, especially when I've been the source, really kind of merged those two things together and I think it's created a confusing messaging. Now, if you listen to all of my exact words I say in the video, it is spelled out what is speculation and what isn't, but because it's mashed together, it can be hard for just somebody who's casually listening to really discern the difference between what's real information and what is just speculation. And I think that people like Nate the Hake can probably appreciate how hard that is to find that balance when you're talking and giving opinions and doing podcasts and stuff. So again, that is something I wanna clarify better and I'm gonna do it probably with some timestamps in the future being like, this is what the actual news is, this is my thoughts and the timestamp will explain that my thoughts are my own opinions and all that stuff. So that is something I need to do better as well. I don't think this really pertains to this Nintendo Direct situation, but just for other situations coming up, like we'll switch to be revealed in March. Again, our two sources, our two primary sources on that are Nate the Hate and Necro Philippe Lima who now I don't really cover him anymore. And then Nate the Hate, who I do fully trust, but also, hey, we didn't get that direct this week. Then again, he wasn't as confident in this week. So we just take this all with it is. Maybe Switch Shoe isn't being revealed anytime soon. Now you might ask what my opinion is on that. I do still believe Switch Shoe will be announced in March, not just because of my retail pre-order thing that I talked about two weeks ago, but actually just because I think it makes sense. And if there's no direct this month, it actually makes even more sense to me, but what do I know? I don't know anything officially. To be clear, I am not Nintendo. So what did we learn in this video? One, we have an update with a new rumor about a direct, I know, it's gonna feel like goalposts moving. We also learned that I had to take some accountability for the way I've delivered the messages at times. I don't think, I don't really feel like I've lied. It's more of a, I have unintentionally, completely unintentionally, maybe misled people by not clarifying the difference between what the report and what the rumor is versus what my opinions are on that stuff and providing counterpoints. And obviously that I need to be much more careful about who I'm trusting to report on. Again, no hate towards the people that I'm no longer gonna be reporting. There's some of you that after I said I wouldn't report on Zippo anymore that said you still trust Zippo. And that's totally fine. I'm not here to tell you who to believe. I'm just telling you how I'm gonna handle things here moving forward. I need to make sure that I can verify these sources in as best as I can. And the only way I can really verify it since I don't have like Nintendo employees I can reach out to is to simply see if they are correct about a number of things and then decide how many things they need to be correct about for me to be able to cover them. All right, I think that's it. I think we're good. This was a longer video than I planned. Very just talking, not a bunch of editing. I just wanted to be upfront and honest with my community. We'll be back a bit later because we're gonna be live streaming the Xbox Direct today, not Xbox Direct, sorry. The Xbox Podcast, right? Because apparently, according to Jeff, yeah, they might have moved the Direct because of it, which suggests this Xbox Podcast might be a very big deal even for Nintendo because Microsoft is a partner. And then on top of that, we have our Nintendo Prime Podcast tonight where I'm sure some of this will come up again. Thank you guys so much for being here and I'll catch you in the next video.


These are the American Gladiators and the events they compete in are confrontational. American Gladiators aired in syndication weekly from September 1989 to May 1996 and matched a cast of amateur athletes against each other as well as against the show's own Gladiators in contests of strength and agility. Joe Thysman and Mike Adamele co-hosted the show during the first half of its first season with Thysman presiding over the proceedings and Adamele serving more of an analyst's role. After Thysman left the series, Adamele became the lead commentator and remained in that role for the remainder of the series. Todd Christensen was initially Adamele's replacement as analyst with Larry Kassanka joining the series at the beginning of season two in 1990. Kassanka was replaced by Lisa Malosky following the fourth season and she held the analyst position for seasons five and six. Danny Lee Clark who spent the first three seasons and most of season six on the show as Gladiator Nitro became co-host for the final season and was credited on air as Dan Nitro Clark. The first half of the first season also had a referee who wore an executioner's outfit portrayed by former football player Jeff Benson. NFL referee Bob McElway then became the referee for the second half of season one followed by Larry Thompson a former Pacific 10 football referee who took over for season two in 1990 and remained until the series ended in 1996. The referees were assisted by several game judges including Bob Wucatich, Fred Gallagher and Jim Marcioni. The contenders competed in a series of events during each episode. Six to eight events were played per show varying from season to season. In each of these events the contenders would earn points based on their performance. Each season consisted of a lineup of four events. Lineup number one consisted of pyramid, hangtuff or assault, joust or whiplash, gauntlet or tug of war, snapback and powerball. Lineup number two consisted of swing shot, breakthrough and conquer or assault, whiplash or tug of war, snapback, pyramid and joust or gauntlet. Lineup number three consisted of power ball, whiplash or hangtuff, sky track, swing shot, assault or breakthrough and conquer and joust or gauntlet. Lineup number four consisted of swing shot, tug of war or whiplash, the wall, hangtuff or assault, power ball, breakthrough and conquer or the gauntlet. The eliminator was the final event played in each episode and determined which contender would win that day's competition. The contenders competed side by side to complete a large obstacle course as quickly as they could. American Gladiators was originally created in 1982 by Johnny C. Frereau and Dan Carr. Carr recruited the Gladiators and hosted the show and Frereau financed and produced the original competition at Erie Tech High School in Erie, Pennsylvania. So Frereau could have the event on film as to shop the new creation. The original six Gladiators consisted of Darren Malibu-McBee, Marissa Lace-Pair, Michael Gemini Horton, Ray Zapp-Hollett, Dan Nitro- Clark and Cheryl Sonny Bardlinger. Malibu went on to appear in the movie Mortal Kombat Annihilation as Motaro and then appeared in 30 other movies and television shows. Lace went on to appear in a number of television series and was one of two Gladiators to pose nude in Playboy. Drawing upon her experience in interior design who once decorated the home of actor Bruce Willis, Lace seemed at home in the arena especially when it came to assault and hangtuff. During her residence between 1989 and 1992, Lace's beauty waved with her tenacity and fierce competitive spirit made her popular amongst fellow Gladiators and fans alike. Gemini was named for a split personality of calm one minute and violent the next. Gemini served as team captain of the Gladiators during his 80 episode run on the show. He would later make appearances on Renegade, Night at the Roxbury and What is Love. Zapp played a reporter in 1997's Letters for Me Killer starring Patrick Swayze. She was also in several other small movie and television roles as well as being the only other Gladiator to pose nude in Playboy. Born in Wilkes Barre, Pennsylvania, Ray Holland was a female bodybuilder performing in season one from 1989 to 1990 and returning in season three for several more years in the role of Zapp from 1991 to 1995. Her bodybuilding career saw her place in many California and National Physique Committee competitions including being named the 1998 Los Angeles overall champion. Her body has graced the covers of numerous fitness magazines including Women's Physique World, Muscle Mag International, Even Playboy. Her success as Zapp also led to guest roles on a handful of TV shows such as Jag and Baywatch. Nitro has been one of the busier Gladiators since the show went off the air. He's appeared in TV shows and movies like Walker Texas Ranger, Ellen, Saved by the Bell and Equilibrium. As a former professional defensive lineman for the NFL's Los Angeles Rams, he was one of the most feared Gladiators. His no holds barred personality paired with his unstoppable physique allowed him to dominate the Gladiator arena between 1989 and 1992. After returning for a final on-court season as a Gladiator in 1994, Clark segued his expertise in the arena to a commentator role during the series final season. Dan Clark continues his career in Hollywood as a jack-of-all-trades writer, director and producer. In 2008 he served as a consulting producer on the American Gladiators relaunch. Sonny disappeared from the spotlight after sustaining an injury during her first and only season on the show. Other Gladiators through the series run included Blaze Bronco, Gold Jade, Laser Titan, Diamond Ice, Thunder Turbo, Storm Tower, Viper Atlas, Cyclone Electra, Havoc, Lace 2, Saber, Siren, Sky, Dallas, Hawk, Rebel and Tank. American Gladiators went on to produce a video game for the Amiga, Sega Mega Drive, Genesis, Super NES and Nintendo Entertainment System in 1991 by Incredible Technologies and even produced a toyline by Mattel. A kid version of the show called Gladiators 2000 hosted by Ryan Seacrest and Mariah Sansone later Valerie Ray Miller in season 2 aired from September 9th 1994 until May 5th 1996. American Gladiators season 5 grand champion Peggy Odita served as head referee. In Gladiators 2002 teams of two child competitors would team up with two Gladiators as coaches and compete by running through a series of events and answering questions on various subjects along the way. While some props and sets were retained the rules for each event were drastically altered. In 2008 a revival of the show aired on NBC from January 6th until August 4th and was hosted by Hulk Hogan and Layla Ali. It was produced by Reveille Productions and MGM Television for mid-season debut. The first ad for the revival aired during the Macy's Thanksgiving Day Parade on November 22nd 2007. The revival only aired for two seasons with a total of 21 episodes ending on August 4th 2008. As of August 2018, Seth Rogen and Evan Goldberg had plans for an American Gladiators reboot. The original series went on to inspire other sports entertainment shows like Battle Dome, Wipe Out, American Ninja Warrior and Dwayne The Rock Johnson's Titan Games. Who was your favorite Gladiator? Do you remember watching the show through the 90s? Personally I would have loved to test myself on there especially during the Eliminator. Did you ever fantasize about appearing on there back in the day? Leave your memories in the comments below. If you enjoyed that video make sure you hit the subscribe button right there so you stay up to date on all things geek culture. Also go ahead and check out one of these two playlists on the side for more videos just like the one you just watched. I'm Shane and for Comic NTV the only place on YouTube where all geek culture collides. Take care Geeks!


Now so far we've just been playing audio through the audio clip of an audio source playing on a wake But of course what we more often want to do is programmatically trigger when sounds play in code and we can do that through the methods of audio source Including play pause unpause and stop which are pretty self-explanatory, but there's also play delayed where you specify time and seconds to wait before starting the sound and Play one shot the regular play method plays the clip specified in the audio clip property of the audio source Whereas with play one shot you can just specify any clip to play through that source And you can also specify a volume scale for that for that clip So in fact with play one shot you can have multiple sounds playing simultaneously through one audio source If we have multiple sounds going and we hit pause they all get paused and we'll all be resumed with unpause And if you call stop all sounds currently playing through an audio source gets stopped There's also the static method play a clip at point where you don't even have to have an audio source to play an audio clip It'll just play at that position in space as specified here though understand with this method because there's no actual audio source You can't feed the output to a mixer. You can't specify its pitch or any of the spatialization properties So it's a much more limited way of playing a sound though in some cases. That's all you need So now looking back at our script We have two clip properties clip one and clip two and an audio source property And so on our object, which has an instance of this audio demo script We hook up clip one and clip two with two audio assets and we hook up the source to be audio cube gray That's this gray cube in the scene which has its own audio source So now we'll have two audio sources in the game the red one and the gray one So when this instance of audio demo is created Unity will take these sound files and create audio clips which it will set to clip one and clip two And it'll take the the audio source of that game object and set it to this source property And then in our update when the user hits alpha one We'll use play one shot to play clip one on source when it alpha two that plays clip two on the source the gray box When I hit Z it invokes the play method on the source X will be pause C will be unpause and V will be stop So now if we go back and play the game We have tinny Prokofiev coming out of the red cube come over to the gray cube and if I hit one We get gongs. I can hit it multiple times and it's just overlapping gong sounds You can't tell do super well, but they're overlapping I'm gonna hit V to stop all those and If I hit Z to play Well the clip associated with this gray cube is Let's see which one we set that to be we said that'd be Beethoven Oh, they're audio source. Yeah, it's this Beethoven I'm gonna hit V to stop and if it to clip two was set to be a different audio clip. It's this right game music I'll get further back. So it's not so loud If I hit X it pauses Z will unpause if I do some gongs and pause and Resume notice the the gong sounds everything paused everything coming out of the audio source paused and then it resumed and Likewise if I bunch of gongs and hit V they'll all stop together So stopping stops everything being emitted through the source all the clips playing Yeah, and also understand if it's Z to play Plays the Beethoven if I hit it again It effectively jumps back So for the one audio clip clip Repeatingly playing Sets it back to the beginning, but that's not the case if I do play one shot So hit two here. I'm gonna stop and hit two multiple times. So first once And then again and it's the same clip overlapping. They're both playing simultaneously very annoyingly. So I'm gonna stop Okay. Yeah, so That one special audio clip properties its behavior is a little different in regards to how play works So be clear that for any audio source you don't really have to set the audio clip to anything you can just leave it to none and You can just use the audio source to play with play one shot instead of ever using the play method and In some cases that's appropriate because maybe you have many sounds coming out of one position in space Though if you want to independently control various properties of how the sounds are played you're gonna need multiple audio sources and Do understand that you can give multiple audio sources just any one game object So you can have as many audio sources on this one game object as you like and that way you can configure them independently So they have different settings and you'll have more control that way Also understand that loading audio clips in this way This is the easy way to do it for sure and it's probably what's most commonly done but sometimes you want to have control over how exactly the audio is loaded because maybe you want to manipulate in some way and Sometimes you want to actually procedurally generate audio data rather than loading it from any file So in that case there is a way to manually create audio clips There's no public audio clip constructor So you can't use new to create audio clips But there's a static create method which you use and then I won't go to the details But there's a way of then loading audio data to create your audio clips The way we did it though is of course much more convenient because doing it this way Unity will load the audio asset and make an audio clip for us So now I've removed all the mixers, but there's another way of applying effects to your audio sources You can add a filter component here I'll do a distortion filter on this red cube And because it has an audio source this audio filter applies to that audio source when it plays sound Let's see. Let me set distortion level something more noticeable Point eight there. Let's see. So now if we play the game Yeah, it sounds pretty distorted to me so there's a distorted Prokofiev and Understand you can also apply these filters to the the audio listener game object and it'll affect everything that reaches that audio listener so here if I add a Echo filter, let's see that should add up pretty decent echo. Let's hear Yeah, it's pretty acuity though understand that these filters don't do anything we can't do with a mixer Mixers are actually just a more general and flexible version of accomplishing the same thing and in fact you'll notice the list of Filters is relatively limited there were more effects for mixer groups than there are filter components Because filter components are actually the old mechanism Mixers and mixer effects are the new mechanism the more recent thing So they're they're generally what you prefer in a modern game though sometimes arguably these filters are just more convenient to use so maybe you'll still use filters, but Mixers really are the more modern mechanism Lastly, let's add here an audio reverb zone create a game object with an audio reverb zone component and It doesn't show up particularly well here But if you zoom out it will see there's a radius is this light blue outline of two spheres This is showing the interior radius the min distance radius This is the max distance radius and the idea is that You know, let me actually shrink these downs. So it's more noticeable effect There I'll try and position that between the boxes. He ends about right There we go, and we'll shrink that max distance a bit too. So we start outside of it So this is defining a bounding sphere in which these reverb effects start to apply when the audio listener enters these spheres and Within the min distance sphere, it's the full effect Whereas if we're in the outer sphere, but not the inner sphere, then it's a it's partially applied When we enter the max distance radius, that's when the effect kicks in and the closer we get to the min distance radius The more pronounced the effect. So we have various different reverb presets and we want the effect to be quite noticeable So I'm going to make it Underwater that one's quite noticeable that we have to do one more thing here for our two audio sources The reverb zone mix if it's set down to zero then reverb zone has no effect. So we obviously want that to be Full effect. Actually, I don't know why it goes beyond one. But anyway, it does so I'll make it one Same thing here. I'll make this one And now we'll play the game We're starting outside the reverb zone But I'll enter Well, I can definitely hear it on my footsteps and I can kind of hear in the Prokofiev Yeah, it's kind of there. It's more noticeable with the lower frequencies that occasionally kick in. Let me try the gong Yeah, that sounds pretty underwater to me I'll stop that and then Yeah, the reggae is pretty underwater too so Because our audio listeners inside that reverb zone, that's why we're hearing that effect applied to all the the sounds that reach our listener At least the ones where the reverb zone Mix is non-zero Now it may have occurred to you that these reverb zones are spherical But what if you want to have a reverb area, which is not a sphere? Like say if you have a rectangular room if I enter the room the reverb should kick in But it shouldn't reverb outside that bounded space that rectangle So it's a little awkward if you try and solve this problem using reverb zones You can kind of hack around it by using triggers to enable and disable your reverb zones, but it's a hacky solution I think the best solution is well in audio mixers We have an SFX reverb effect which has all the same effects we can apply so we can apply any kind of reverb through audio mixers that we can do with reverb zones and So rather than using reverb zones at all We just have trigger colliders which when our audio Lister enters those trigger colliders the trigger will enable these reverb effects on our mixer So we can get reverb without reverb zones entirely And if you really want to do this properly you would have a transition threshold where you have the interior trigger space But then a trigger threshold like when you go through the door such that you would do the Calculation of well how close am I to the reverb zone and within a certain distance It'll kick in some reverb until eventually hitting the full reverb when you enter the full trigger zone So again, we actually really don't need reverb zones We can get the same effect using mixers and trigger colliders And that generally I'd say is actually the proper solution in most cases because the common case where you want reverb is within Rooms and rooms are usually rectangular So it's just a lot less clumsy if you can define precise spaces Rather than trying to approximate with spheres which can get pretty clumsy quite fast


What are your thoughts on? Very block being responsible for almost one quarter of Bitcoin transactions in January by using the up return script for proof of proof This is a question by Jonathan I'm not familiar with the case of very block, but nevertheless Let's let's assume that that's an accurate representation and very block is indeed using one quarter of all Bitcoin transactions in January Jonathan asks could this and other such uses of the Bitcoin blockchain have an impact on the fee market such as it affects the use of Bitcoin as money. This is a great question because this thing comes up a lot What is a valid transaction? What is a spam transaction on the Bitcoin system and the answer is really simple We have two ways of determining whether a transaction should and should not be on the Bitcoin system One possible way to do that is to set rules in the protocol that make a difference between What is spam and what is not spam? basically allow the developers of the Bitcoin core protocol to pick and Choose winners and losers by determining which applications should innovate and which should not based on some determination qualitative normative judgment of What is a valid use case of Bitcoin and what is not and you might think that that's an easy answer Money is the right thing. Everything else is superfluous extraneous not really relevant But then again, which applications of money is is multi-stake money enough or is that fancy scripting and programming? What about lightning network should that be allowed maybe some of the original core developers are not so fun not so interested in Lightning, what about time locks and other things like that? What about other forms of smart contracts? This is a very slippery slope. So in in Bitcoin today We use a market-based mechanism and the market-based mechanism is really simple The fee market enables pricing of transactions based on supply and demand that allows the market and Especially the sender of a transaction to signal to the network through their selection of fees What importance that transaction has to them? How important that transaction is to them and thereby pricing the cost of Transactions space across the entire market vis-a-vis other applications that might not be as important and what this is? Pricing is not just whether the transaction is Confirmed or not, but more importantly how fast the transaction is confirmed in this particular case The market is pricing very blocks transactions Which are using one quarter of the Bitcoin blockchain for proof-of-proof and Apparently that's how much of the capacity the market is pricing to allocate in that particular application Does it affect the use of Bitcoin as money? It certainly prices that scarce resource and what it does is This fee market prevents people from attacking the network with denial of service attacks and spam attacks because it causes A cost because it makes it costly to post transactions that are not important to the sender So spam is expensive on Bitcoin because of transaction fees and that prevents attacks against the network I haven't had any difficulty making my transactions I haven't had any difficulty making them on the Bitcoin blockchain with Segwit I haven't had any difficulty making them on lightning and opening and closing channels I always use the absolute minimum fee possible what Satoshi provides I Use replaced by fee transactions just in case I want to bump the fee later because it's not going through but honestly I haven't bumped a fee in six months or more and The transactions I make which I make very regularly on a weekly basis get through within the first or second block so is this a problem for the Bitcoin network no it isn't and There's nothing wrong with using one quarter of all Bitcoin transactions as long as you pay for them The the issue here is that we need to understand that in the absence of a fee market What is the alternative in the absence of a market-based solution to? prioritization and capacity management Resource allocation within the Bitcoin blockchain we can do one of two things one we can assume that resources are infinite or near infinite and that Just giving free transactions to everyone will not have any economic impact What that will do effect is effectively is it will subsidize those who are sending transactions and It will subsidize miners through other means probably inflation and cause further Centralization of nodes and more importantly mining to fewer and fewer hands So there is a cost instead of paying that cost in fees to maintain Decentralization you pay that cost by losing Decentralization behind the scenes in a subtle long-term way that is less easy to detect that is a very dangerous path And we've seen other blockchains try that so it's okay If you want to try that method you can always choose one of the other blockchains that does it that way The other option is to substitute market forces with centralized control and decision-making by committee to give developers the power to choose what is and isn't a valid transaction Both of those choices are inferior to market forces So I don't think there's anything wrong with anyone using whatever capacity of the Bitcoin blockchain They want to for whatever application they want to as long as they're willing to pay the fee and compete in the market


Art wasn't one of the things that I found. I think art found me. My name is Brian Poli Dixon and I'm an artist. I started painting five years ago. You know, I was playing football. I went to college at UCLA, played football there. Then went to the NFL after that. Only after I retired from the NFL did I discover painting. It really was just a natural progression. It was one of those situations where I've always felt like an artist. So I feel like I was an artist before I was an athlete. My process when I'm creating work is a little bit different for each painting. There are times that I have absolutely no idea what I'm gonna do when I start the canvas. And I just literally put paint on the canvas and I find the painting as I'm going. If you went into one of my shows, as me as an early artist, it would look like there was five or six different artists on the wall. It's fun. It's like an experiment all the time. So like, you know, you're working with different mediums, different paints, kind of seeing what works what doesn't work. You know, it's just kind of like learning on the go. If I'm doing a painting that is part of a series, then I kind of have an idea of what I'm gonna do before I start. I'm constantly, you know, writing down dreams or ideas or quotes and all this kind of stuff. And my genius series that I'm doing is very special to me. Most people, when they think of genius, they think of somebody being like super smart. But for me, genius is just having something that, you know, is special. Or almost like a passion or a purpose. So it's something that everybody has inside of them. You know, once you find your genius, you know, try to share that with as many people as possible. If you want to be a professional artist, it's not just about painting something and having it on the wall. So when you have a website, you have the social media platforms, you're doing shows. It makes people think that what they're buying has value. The thing I like about social media is the fact that it's all real time. You're kind of keeping people engaged and it makes it more fun though too. You know, honestly, like, I think sky's the limit. I'm constantly pushing, constantly working. I'm just really excited, you know, for what's ahead and I don't even know what that is yet. When I get to see a finished product and it's in someone's home or it's in a gallery, that's probably the best feeling. That's what I consider success.


Welcome to the exam review for exam 2 for math 1220 calculus 2 for students at Southern Utah University. As usual I'll be your professor today, Dr. Andrew Missildine. So in this video I want to quickly talk about the contents of exam 2 for a class to give you the students an idea of what you should be studying for and how to better prepare for this exam of course. Now there are some specific information you definitely need to know about the exam like the time place manner which it's gonna take place but as these change from semester to semester that will not be included within this video. So things like what materials am I allowed to use during the test, when will the test take place, dates, those type of things. Please consult the exam syllabus that can probably be found on Canvas for the semester specifics. This video is just gonna focus on the structure and contents of the exam. Just so you're aware exam 2 is gonna cover materials from lecture 10 all the way up to lecture 21. So a quick summary of what's gonna be on this exam is there'll be techniques of integration. So this will include many of the new techniques that we've learned about like we've learned about trig integrations. So how we can use trig identities to help us compute anti-derivatives of trigonometric functions. But we also have trig subs that we've now learned about how the method of substitution can be modified to turn algebraic functions into trigonometric functions and use the techniques about trigonometric integrals to help you in that setting. We of course also have our partial fraction decompositions that help us with rational functions. We have things like a rationalizing substitution. But we also have some of the more classic materials techniques we've learned about previously like u-subs are still perfectly valid here. Integration by parts of course is also a valid technique that we need to be aware of. And so and then of course you can put all these together in a street fighter manner. And any of these techniques could be used oftentimes in combination with others. And so the vast majority of the test is gonna be about these techniques of integration. Now of course some other things that should be mentioned topics of numerical integration will also be covered here. Midpoint rule, trapezoid rule, Simpson's rule, improper integrals will also be discussed on this exam. And then also we have two applications of integration that will also appear on this exam as well. This includes arc length and surface area. And so let's say a little bit more about these topics in just a second. I do want to mention just like exam one there are going to be three sections on this exam. There's the multiple choice section, a short response section, and the free response section. The structure and policy related to these types of questions are identical to the previous exam. There'll be four multiple choice questions worth five points each. There'll be four short response questions that'll be worth seven points each. And then there will be four free response questions. Most of them which are worth 12 points but there is a 16 pointer that'll be coming up. And let's take a look at these topics. All right, so let's start with the multiple choice section. Four questions there, like I said, five points each. The first question that you're going to see on this exam is going to be a question about trigonometric substitution. But all that the question is going to ask you, it's not going to ask you to evaluate an anti-derivative, it's just going to ask you which trigonometric substitution should you use when considering an algebraic integral like this one. Now clearly this comes down to what is the square root doing? We're interested in basically three basic forms. So you have the square root of a squared minus u squared, where a is here a constant number, u is some function. This is like what we use for a sine substitution. We could also look at the square root of a squared plus u squared. That's useful for you would want to use a tangent substitution in that regard.  A secant substitution would be relevant there. But also keeping track of where do all the coefficients go and things like that. Question one, just ask you what is the correct trigonometric substitution you should use to start the start the anti-derivative process. So just the very initial step of a trig sub. There will be another question in the free response that asks you specifically to compute an integral using trigonometric substitution. This is just asking what's the very first step. What is the substitution in play? It's a fun question. Question two is very similar in nature that using the techniques we've developed we just ask what's the very first step. So imagine your task to find the anti-derivative of a rational function like the following. This is definitely more complicated than we usually do but this question only ask what is the correct template of the partial fraction decomposition. So we care about the factorization of the denominator. So do we have linear factors and how often do they show up? Do we have irreducible quadratic factors? How often do they show up? In which case we need to have a partial fraction for each of the powers there. So like with an x squared on bottom you have a partial fraction for x and for x squared. Similar thing can be said for x plus 2 squared and then for irreducible quadratics you have to deal with those as well. For a linear denominator you should have just a constant on top. For a for a irreducible quadratic you should have some type of linear factor on top. dx plus c or something like that. And so question two is again just a starter question. You don't have to do the complete partial fraction decomposition. All that you have to do is determine what is the right template to get started. Now if you need a review of any of these topics here remember that the topics of partial fraction decomposition were covered in lecture 14 and 15. And then likewise topics of trigonometric substitution were discussed in lessons 12 and 13. Please go back to your notes on those topics if you need some more assistance. For example the codex was introduced in lesson 12. That's exactly what you need to use for question number one. Question number two we saw we saw linear factors show up in lesson 14. Irreducible quadratics showed up in lesson 15 so you'd want to consult both of those there. So then coming to question number three. Question number three is going to ask you to compute a numerical approximation of an integral using one of these numerical integration techniques like the trapezoidal rule is a possibility the midpoint rule, Simpson's rule you should know all three of those rules here. Now how this question is going to be formatted is that your function is going to be given actually as a table. So we see the x coordinates are given here and then they're corresponding f of x values are given there as well. So the way you would read this is that f of 10 is equal to negative 12 and f of 22 is equal to 1. Using this table you'll be asked to approximate an integral in this case you're integrating from 10 to 30 and you're going to use five subdivisions in that regard. You want to use the and for this one you're going to use the trapezoidal rule t5 to then estimate what is the area under the curve. You're going to estimate this integral. Be aware that the way that this question is formatted you won't be given an algebraic function. You cannot use the fundamental theorem of calculus to evaluate this integral. You actually only have enough information to approximate it using the method we're introduced here trapezoidal rule midpoint rule or Simpson's rule are all possibilities here. Now if you need some more practice or need a review what's how these calculations are actually done as a reminder lesson 17 reminded us about the trapezoidal and midpoint rules and lesson 18 was exclusively about Simpson's rule. You'll probably want to go to both of those for some further practice there. And then the last question in the multiple choice section will be you'll be asked to evaluate an improper integral. So these are the cases we have integrals where one bound goes off to infinity or negative infinity maybe both or maybe the integral approaches a vertical asymptote and so how do you how do you deal with improper integrals? This is exactly what we learned about in lesson 19 and so question number four will ask you to compute to evaluate an improper integral. Be aware that the answer could be that it's divergent. If the integral is divergent that is the area under the curve goes off towards infinity you would select choice f that it's divergent but if the integral is convergent then you have to actually provide what was the value it converges towards and so then you would say whatever you think it is pi over two or whatever. Moving on to the short response section remember there's four questions here and each of them are worth seven points each. Question number five will be a second question about numerical integration and this will be the last question on the test coming from numerical integration. What it's going to ask you to do is to work with the error bounds associated to these numerical estimates. So the trapezoid rule has an error bound the midpoint rule has an error bound simpson rule has an error bound. I recommend you turn to the study materials or to your notes to find the exact formulas for those error bounds but let's say that we were working with an integral let's say the integral from zero to one of cosine of x squared dx. Be aware that that would be a very difficult function to find an anti-derivative for but we could estimate the area under the curve using something like the trapezoid rule but how do we know we have a good enough accuracy? Well this question asks what choice of n what's the smallest choice of n to guarantee that the approximation is accurate to four decimal places? Well there's an error bound associated to the trapezoid rule you would use that to solve for n remember you're always had to round up in that situation for simpson's rule you always have to round up to the next even integer because for simpson's rule it always has to be an even number there. These error bounds will be dependent upon how large second or fourth derivatives are equal to so for convenience you might be given information about the second or fourth derivative so that the exercise focuses on the error bound and not on the the implicit derivative calculations that are necessary as well. So like this one's format in such a way that the k value you can actually argue a six and that will help you when you try to determine what is the best choice of n in that situation. So these type of questions about error bounds showed up in these numerical approximation sections so again like we saw in the previous slide lesson 17 will give you the error bounds for the midpoint rule and trapezoid rule lesson 18 will give you the error bound for simpson's rule you should be prepared to do any of those three. Question number six you'll be given a trigonometric integral and you'll be asked to find the antiderivative of that trigonometric integral and it could be anything under the sun it could involve signs and cosines the periods could be the same the periods could be different it could involve secants and tangents I mean maybe even cosecants and cotangents right we've learned all about these techniques we should be looking for things like is there an odd number of cosines an even number of cosines odd number of signs an even number of signs tangents and secants similar questions can be asked there a whole litany of trig identities come into come into play there question six will be about any one of those what any one of those type of calculations this is the only question on the test that directly comes from lessons 10 and 11 just as a reminder lesson 10 was actually broken up in two pieces the first half ended our lesson about integration by parts but then the second half then introduced our topic of trigonometric integrals there's some important examples and identities found there lesson 11 then continued and then finished this discussion about trigonometric integrals so like I said question six is to be the only question on the test that comes directly from there but like I mentioned earlier there will be a question in the free response section about trigonometric substitution the whole method of trigonometric substitution is to turn an algebraic integral into a trigonometric integral and so all the techniques that are applicable here will be applicable there as well and that's why I only put one direct question coming from lessons 10 and 11 because the trig sub questions will ask you to do similar information as well now this is an indefinite integral do remember that whatever you calculate you do need a plus c there for full credit so don't forget that c the other two questions on the show response section are going to be questions that ask you to set up simplify but do not evaluate an integral and these are going to do with our two application topics question number seven is going to ask you to set up an integral to compute the arc length of some curve question number eight will similarly ask you to set up an integral that computes the surface area of some surface of revolution like we did of course in sections let's see what the the lesson numbers were lesson 20 for arc length and lesson 21 talked about surface area you're going to want to go to those lessons your corresponding notes the sections from the book in order to find the appropriate formulas for that situation do be aware that you asked to set this thing up so when you set up an integral you do of course need the integral symbol you need to have the the appropriate bounds a and b there needs to be of course a function and that function might be multi-part because of the formulas in play there like for example for surface area in addition to having a square root likely be in the integral you also have a radius to deal with there's also a two pi floating around so look for those but you also need to have your differential that is part of the integral it does represent a geometric part of these problems and so omitting the integral would make it incorrect particularly in these examples right here because the default integral you're actually integrating with respect to ds for which ds can be modified into a dx or a dy that is you can integrate with respect to x or y if you don't specify which one you are using you actually can't necessarily glean from the information what it is it could be dx or dy and therefore you need to be explicitly including that in your calculation there i should also mention that you should simplify these things as appropriate now i don't necessarily require every possible simplification under the sun but you definitely got to get all the low hanging fruit ones and just some natural algebraic simplifications are appropriate here you do not need to evaluate the integral there will be no credit given for that but if you're lacking appropriate and necessary simplifications you could lose some points there as well and that then gets us through the short response section the final section of the exam is the free response section there's four questions here now their points change based upon the perceived difficulty of these questions most of them are in the 12 point range though so question number nine is a 12 point problem and i'll ask you to evaluate an indefinite integral now you are allowed to use any technique you want on this problem but be aware that this question was intended to be a trigonometric substitution so things you can do to show your work because this is a free response question you do need to show your work for full credit there you could say things like what is the trigonometric substitution you're using you can say things like well x equals a times whatever the trig function is let's say it's a tangent substitution i'm not saying that's what the correct substitution is here i'm trying to not give away the answer i want you to work this out on your own but let's say that you think the trig sub is x equals a tangent then you could be like well dx equals a secant squared theta d theta you can then also tell us about the square root the square root of a squared plus x squared is equal to a secant this is all very important information you can then also if you want to you control the triangle not necessary but this is one way to show your work if i have a tangent substitution i might say x over a the square root of x squared plus a squared like so then once that's done of course you can start doing your substitutions there you can be like oh well x squared is a tangent squared now the square root is then a secant again i know i'm not actually doing the wrong problem this is just for illustrative purposes here the dx would be like a secant squared theta d theta then you proceed to simplify this thing compute it but at the end you should probably switch it back into some antiderivative in terms of x unless it's a definite integral if it's a definite integral then of course you can switch the balance and find the number using the trig metric function but most likely this will be an indefinite integral so the variable if you have some function in terms of theta that you would find here that's good partial credit but for full credit you do need to switch it back to the function of x and as this is an indefinite question indefinite integral you need that plus c for full credit there so there's a lot going on because you have to convert from algebra to trig solve the trig antiderivative then switch it back from trig to algebra there's a lot of stuff going on there which is why this is worth so many points 12 points there and also just as a reminder I mean I've already said in this video but in case you missed it before let me just remind you again that the topics of trigometric substitution are discussed in details in lessons 12 through 13 the next question number 10 it's also worth 10 points and it's of comparable difficulty to question number nine the difference now though is that we are given a rational function and so you're going to want to find the antiderivative using the method of partial fraction decomposition as discussed in lessons 14 and 15 and again this one question could cover any of the topics that we've seen using partial fractions so in particular if I was to get started with this there's some things you should look for you might need to use long division that is division of the polynomials this happens in particular if the fraction is improper that is the numerator is bigger than the denominator the example on the screen right now seems to suggest you might need to do that it might also be necessary to complete the square because you do have to sometimes deal with these irreducible quadratics in order to prepare for a tangent typically but it could be a sin or secant as well in order to prepare for a trigometric substitution you often have to complete the square be aware that this is an algebraic skill that might also be necessary on question number nine you might have to complete the square before you can do the substitution clearly factoring might be an important thing that has to happen in this situation can you factor the polynomial denominator I won't make the factorizations too difficult but pulling out things like a greatest common divisor our common factorization forms like uh difference of squares perfect square trinomials maybe like factoring by grouping there are some elementary factoring techniques that uh we're on the on the par of like intermediate algebra math 1010 that would be appropriate and be expected of students to know here so there are some algebraic things you have to do there then of course you're gonna have to do the partial fraction decomposition itself come up with the correct template like we do on question number two from the multiple choice section solve for the coefficients now as you're solving for the coefficients and your partial fraction decomposition of course you can use this technique of annihilation where you choose strategic cool values of x to eliminate everything except for one of the parameters that's acceptable you could set up a system of linear equations and solve it you could do a combination of those two methods however you find the coefficients as long as it's done correctly i don't care how you do it so you'll need to find the partial fraction decomposition and then at the end you do have to integrate the function itself if you've computed the the pfd it shouldn't be too hard to do um you'll have some standard forms there uh typically the anti-derivative involved logarithms and arc tangents that come from u substitutions those are often necessary in the situation um likewise you might have to do some trig subs when you have irreducible quadratics and so just some things to remember here it might be useful to observe that if you have a function of the form du over u this is equal to the natural log of the absolute value of u plus a constant that does show up with enough frequency that it's worth mentioning i should also mention that if you if you have the integral du over a squared plus u squared where u is some function of x a is a constant the anti-derivative in that situation is going to be one over a arc tangent of u over a plus a constant these two anti-derivative forms are of some common frequency when you're dealing with partial fraction decompositions it might be worth you know memorizing these are put in a reference that you can find later on all right let's now move to the last page of the exam so questions 11 and 12 uh question number six sorry question number 11 is worth 16 points um it is the climactic question of this exam and this question is supposed to represent our street fighter integral question that we learned about of course in the lessons here where anything goes on this one as opposed to questions nine and ten where i then i i i i prophesied to you what the topics are going to be you're going to use trig subs on number nine if you do something else you're probably making it harder than needs to be on question number 10 you're going to use partial fraction decomposition of some kind and again if you don't then you're probably doing it wrong not necessarily but you're definitely making it harder if you're not with question 11 anything goes anything goes anything goes so this involves any of the topics that we've learned about now the specific lesson about these about street fighting was lesson 16 which we talked about techniques of integration for which remember those techniques i mean sometimes the right thing to do is some type of algebraic manipulation use algebraic identities to help you out here um that is certainly a possibility here uh but also by the nature of the problem maybe it's trigometric or maybe you do a trig metric substitution um trigometric identities may also be useful in this situation again you might want to go back to lessons 10 and 11 to review some of those topics but like i said you also can use substitution of course the topic of you substitution is perfectly relevant here that actually goes back to lesson two for this for this lecture series here old topics are just as valuable on this example as well so speaking of which we could talk about integration by parts integration by parts was introduced in lessons nine and ten integration by parts might be necessary to work on these type of problems um in addition to trig subs uh excuse me in addition to u-subs you might have to do a trig sub this one i'm looking at i don't see any sums or differences of squares so probably don't need a trig sub but maybe um which of course i've already said it twice but i'll say it one more time trig subs were introduced in lessons 12 and 13 here that might be very very appropriate to use of course methods of partial fraction decomposition might be very relevant for this one which again that was lessons 14 and 15 how do you deal with partial fractions just much like we did in question number 10 there but also an important topic to pay particular attention to in lessons 16 we actually focus a lot of time on a method known as the rationalizing substitution for which you do basically a u-sub that turns your function into well into basically a partial fraction well that is a rational function for to do partial fractions decompositions and this is very useful when you have a substitution like u equals the square root of x um because in that case you get that du is equal to well i'll actually say this way you get that dx is equal to two u du the derivative of the function is actually like similar to the original function itself and that can be very useful this also happens with like exponentials if u equals e to the x then du equals e to the x dx for which that tells us that dx is equal to du over u things like that so this rationalizing substitution is very useful with radicals and exponentials because of the similarities between the functions and its derivative and so when i look at something like this my thoughts are maybe a rationalism substitution could be very useful here but honestly anything can go this is why this question is worth so many points do not give up on this question even if you're stumped that is too many points just to throw away um work at it do what you can play with multiple attempts um you can definitely get some partial credit even if you don't do it all the way um don't forfeit this question it's a very important one and it really much is going to characterize how one does um these techniques of integration the last question uh question number 12 it's only worth 10 points here not as much as the other three certainly um and this is actually a question about improper integrals we have one question the multiple choice there'll be a second one right here in this situation you'll be asked to show that an integral an improper integral either converges or diverges it'll tell you whether it's convergent or divergent um in particular this question this function we chose it in such a way that you will not likely be able to compute an elementary anti derivative of that function um so we can't necessarily apply the fundamental theorem calculus directly instead though what we can use as an a theorem we learned about when we learned about improper integrals this is the actually the so-called comparison test remember the comparison test tells us that if an improper integral is smaller than a convergent integral then it's likewise convergent um but also if an integral is bigger than a divergent improper integral then it also must be divergent so that is we can potentially simplify the function by comparing it to something which you know to be convergent or divergent and then use that make sure you state explicitly when is the comparison test being used and so try to mimic some examples uh that we saw of course in lesson 19 and so that gets us to the end of this exam and we've now talked about all the topics that are covered on this exam uh in addition to of course this video use the exam syllabus to practice exam and other study resources that are available to you on canvas if you have any questions please reach out to me or other appropriate sources to get the help you need as you prepare for this exam i'm quite confident that you will be able to do very well on this exam if you are sufficiently prepared for it and let me help you prepare for the exam if you're not there already


So I watched a video recently. It was on the YouTube channel of a guy called Darren Grimes. He's a kind of conservative influencer. He's young and right-wing. That's quite a rare combination these days. So he's gained quite a big national profile for himself. He's regularly on the BBC, Sky and so on and so forth. On this YouTube channel, his first guest is a guy called David Starkey. David Starkey is probably the most successful kind of pop historian in Britain in recent decades. He's been around for a really long time but he's not just somebody who makes these kind of public interventions, political kind of interventions. They're overtly political often. He's also somebody who is viewed by many people as a legitimate historian. You know, he's gone honorary fellowship at Fitzwilliam College in Cambridge. He's got a CBE. All that accounts for much these days often but he's got the credentials. He's very much part of an intellectual establishment as well as somebody who appears on the television. And yet, and yet, I'm going to show you just one minute from that hour-long interview and just in that one minute is contained, I think, some of the most ridiculous, crazy and hinged comments I've seen from a public figure in Britain in a really long time. Watch this. Slavery wasn't genocide. Otherwise, there wouldn't be so many damn blacks in Africa or in Britain, would there? You know, an awful lot of them survived. Slavery wasn't genocide because people survived. There were so many damn blacks in Britain and America and of course, the continent of Africa, hundreds of millions of people. How could it have been a genocide if people survived? Well, Professor Starkey allowed me to introduce you to literally every genocide ever, the Holocaust during the period of the Third Reich between 1933 and 1945, around 6 million Jewish people die. I don't think anybody would contest that was a genocide despite the fact that today there are millions of Jewish people around the world. Who says that isn't a genocide or the fact that towards the end of the Ottoman Empire about 1.5 million Armenians are killed during the Armenian genocide? Because there's Armenia today, nobody says, well, that never happened. That wasn't a genocide. No, it was a genocide. Or what goes on in the Americas? Christopher Columbus discovers, discovers the island of Hispaniola in 1492 has a population of around a million, 30 years later the population of 30,000. Is that not genocide because 30,000 people survived? Or the Americas had 100 million people when Europeans first encountered the Western Hemisphere, 100 million people, these really great complex civilizations, the Maya, the Incas and so on. And it goes. And because today you have a couple of million people of indigenous descent in the country, you would not call that a genocide. So this is the first point. This is crazy because according to this highly esteemed historian who, like I say, is regularly on the television, there's never ever been a genocide because any genocide with any survivors isn't a genocide. Crazy. And what again, there's no point in arguing against globalization or Western civilization. They are all products of it. What is he talking about? Globalization, Western civilization, it's one of those things where people on the right try and basically mystify and obscure categories and they say two things which are completely different and they try and make them the same thing. So people go liberalism and free markets and the Enlightenment. Hold on, these are all the renaissance. These are all completely different things. Globalization is a process of the world getting smaller, a contraction of time and space. We could talk about it emerging with real-time communication. We could talk about it coming out of the 19th century with rail and steam engines and the telegram. Obviously the internet makes that time-space compression even more intense. Or we could go further back, we could talk about the Roman Empire. Or we can talk about the discovery of the Americas by Europeans, the beginnings of European colonialism. Why would you want to start globalization with Western civilization? Think about it. Our numbers are Arabic numerals. We used to use Xs and Vs and 1s until about 500, 600 years ago. Our gods are from the Middle East. Most basic mathematical concepts come out of India. Zero infinity. Are they Western? They've globalized. They've done pretty well. They've traversed cultural norms and borders and boundaries. Why is Western civilization and globalization synonymous? Hidden in terms of what I'm trying to say here, they aren't the same thing. We are all products of it. The honest teaching of the British Empire is to say, quite simply, it is the first key stage of world globalization. It's probably the most important moment in human history. What is this guy on about? The beginning of globalization is with the British Empire. I mean, you can make the argument. I mean, I wouldn't make the argument. You can make the argument. Then he says it's the single most important moment in human history. More important than agriculture 12,000 years ago. Before 12,000 years ago, there were about 5 million human beings about the population of present-day Ireland on the whole planet. After agriculture, you get to 1 billion by 1800. You get to about 7.5 billion today. I mean, I think agriculture and the domestication of animals and crops is probably a bigger historical moment than the British Empire. I could be wrong. It gives us little things like cities and literacy and really complex configurations of society. I mean, I could be wrong, but I'm pretty sure it's a bigger deal than the British Empire. And if you're still with us, its consequences are still on. And generally speaking, in most ways, actually fruitful. There were downsides, again, as the Brexit vote demonstrated. So he's saying, first of all, there's a couple of things here. He's saying that the British Empire was generally good.  Some things were good. Some things were bad. Okay, well, what was bad? The Brexit vote. What? We can talk about some of the bad things that come out of the British Empire. Approximately 35 million Indians or people in South Asia, what was then the Raj, including Pakistan, Bangladesh, 35 million people die as a result of Britain occupying that country. 35 million people. That strikes me as something of a downside when Britain conquers India, so to speak. It wasn't originally Britain. It was the British East Indies Company. It only becomes Britain when you have a mutant in the 1850s. When they do that, India is the world's first or second largest economy. It's one of the wealthiest places on earth. When Britain leaves India in 1947, it is one of the poorest, illiterate countries on the planet. GDP per head in India doesn't move from 1735 until 1945, right? People in this country say GDP per capita per head per person. Oh, it's barely moved for 10 years. Yeah, try 200 years. Try 200 years. And even then in the latter half of the 19th century going into the 20th century, life expectancy dramatically fell. It dramatically fell. So how is this a good thing for Indians? And this was a country which was persistently marked by famine under British rule. This wonderful, laudable, generally kind and beneficent British rule. Well, there were famines all the time. India hasn't had a single famine since 1947, not a single one. During the Second World War, it was subject to the Bengal famine, which was a policy of enforced famine by the British. And today, it's the world's number one producer and exporter of rice. So you've gone from a basket case which couldn't feed itself to a country which is exporting food overseas. Somehow, rather than Britain being good, it seems to me that it was very, very bad for India. And this is just one country. We could talk about Ireland. Ireland today has a smaller population than it did at the beginning of the 19th century. What other country does that apply to? Ireland had more people in the 1810s, 1820s than it does today. Why? Because we had a policy of enforced famine. People had to leave the country. It was made unlivable. You could talk about Kenya. Britain was operating there as a colonial power until the 1960s. Between 1945 and the early 60s, you've got about 1.5 million people have put in detention camps by the British. About 150,000 people die, use of torture. Today, if you fly into Nairobi, you'll probably use Kenyatta Airport. That was built by forced prison labour. Political prisoners who had never been subject to a trial, generally speaking, built the airport. This isn't Stalin's gulag. This is the Brits. Then you've got Malaya. Very similar strategy the British had in terms of putting down the insurgency there. They used a thing called Agent Orange alongside the Briggs Plan, which again was a policy of enforced detention. Do you know who adopted that afterwards? It was the Americans in Vietnam. It was the Brits, however, which pioneered it. So you're looking at East Asia. You're looking at South Asia. You look at Ireland. You look at Africa. None of these places have benefited from the British Empire. I'm sorry, Professor Starkey.  So that's how you go about tackling it. And as for the idea, as I said, that slavery is this kind of terrible disease that dare not speak its name, it only dare not speak its name, Darren, because we settled it nearly 200 years ago. We don't normally go on about the fact that Roman Catholics once upon a time didn't have vote and weren't allowed to have their own churches because we had Catholic emancipation. We settled slavery 200, by the way, it wasn't 200 years ago. Almost 200 years ago. We settled slavery 200 years ago. And he says it's the same as Catholic emancipation. If slavery was settled 200 years ago, can you explain to me why today, the average African American male will live to 72 years of age, which is the same as somebody who lives in Palestine or is actually less than somebody in Cuba, which is a much poorer country than America, right? They'll live less than somebody who lives in certain provinces of India, which are much, much poorer. Why? Because they're African American males, because we still have the legacy of slavery. If slavery was dealt with two centuries ago, why does pretty much every country on the continent of Africa have as their primary export, either an agricultural good, or, you know, basic resources, minerals, or diamonds? Why would that be the case? Why would all these countries in Africa be so poor and be exporting things to be made into more expensive commodities by other people? The reason is something called neocolonialism, right? It didn't just disappear. Slavery became something else. We still have empires right until the 1960s, the 1970s. And even then that carries on through other means. So the idea that we did our thing with slavery 200 years ago, we never need to talk about race ever again.  Even in an advanced economy like America, like I say, African American people are massively disadvantaged. In this country, rates of home ownership amongst black people massively lower compared to the rest of the population. That's before you talk about racialized policing. That's before you talk about experiences of the criminal justice system, et cetera, just in terms of the economic experience within which they're growing up as human beings, completely different. So the idea that we dealt with slavery 200 years ago, therefore it's in the past, and you're comparing it to Catholicism. Are you mad? The countries which went to bloody the Americas and the late 15th century, early 16th century were Portugal and Spain. They were Catholics killing them. So the idea that, oh yeah, these great colonial powers, Spain and Portugal, somehow they were the subaltern. We're going to say, well, we got rid of Catholic laws that prejudiced against Catholic people 200 years ago. Anti-black racism is kind of the same thing.   Because we had about 12 million people cross the Atlantic as slaves, about a million and a half people, by the way, died making that journey, forced to work on plantations for cotton, tobacco, coffee, timber, which was then going back to Spain and Portugal, but you're comparing it to Catholicism.  I mean this just shows me the complete, the terrifying nature of anti-black racism and how permissible it is to apply society. Do you know what? We had Catholic emancipation at pretty much exactly the same time that we got rid of slavery in the 1830s. We didn't go on about that. He's nodding. He's nodding. Darren, if you had any self-respect or an ounce of intelligence, you would say, I don't think it's right that we compare Catholic emancipation to the abolition of slavery and anti-black racism. I mean, unless he agrees with it, right? That's the most worrying part of this. He probably does agree with them. If he disagrees with them, Darren, if you disagree with somebody, you should tell them, especially when they're being a giant racist. Now, like I say, this is just one minute from a 60-minute interview. I could have done a five, six-hour video here, but it's really important takeaway for me is this. David Starkey is on BBC Question Time, he'll go on The Daily Politics, he'll go on Sky, he's hosted his own shows. He's seen as a really legitimate, credible voice on UK politics.  Now, why at his age is he saying these things? It's because he's been unchallenged for a really long time. And you'll notice he comes from a working-class background, but he's very well spoken, and that generally is my analysis, actually, of why David Starkey is where he is and saying the things he's saying.  And I think it's time, we say to people like the BBC, to Sky, to whatever media outlets, look, you can have a range of views, that's great. You should do that. I'm not up for narrowing the scope of debate, but this is crazy.  This is nuts. How is it possible that somebody goes this far overboard? It's because nobody at any time in the last several decades of his career has said, David, enough, you're talking complete batshit nonsense. Maybe it's time you started doing that.