with the 14th overall pick in the NFL draft, the Baltimore Raven select safety, Kyle Hamilton. I remember watching this live and just thinking, wow, that is a very interesting pick and one that I didn't see it coming. I didn't see it coming. We had so many, yeah, a significant amount of questions from subscribers where people were like, what if Kyle Hamilton is dead? Just imagine that scenario of Kyle Hamilton is sitting there. What would the Ravens do? What they actually pounce? You gotta feel like they would, but at the same time, they got other things that they need and they signed Marcus Williams. They still got Chuck Clark. They got Geno Stone, Tony Jefferson, Brandon Stevens, Ardarius Washington. And we know not everybody's gonna make the roster, but still, but the Ravens were like, hold up, generational talent and safety position? Somebody that could really be like that as safety? May need to even play him at some corner as well? No, we not passing on that. So this pick, again, it was very interesting. They get the best safety in the draft. They get him at pick 14. Some people thought that he may go number three overall, number four overall. Most people initially, early on in the draft season, a lot of people thought that there was no way that he makes it out the top 10. Maybe not even the top five, but he made it all the way down to 14. Right at 14. But the pick before, the Eagles, ooh, those Eagles. Ha ha ha ha, mm, it's a game. It's a game, NFL is a game and it is to be played and the Eagles, they jumped ahead of the Ravens because they just knew, they knew. Eagles were like, oh yeah, we'll take a little generational talent of our own. And Jordan Davis, we'll get them right. And then Ravens won't. But yeah, Ravens get Kyle Hamilton. So what does this mean? What would this do for the Ravens? Well, first thing that comes to a lot of people's mind, Chuck Clark, what is going to happen with Chuck Clark? The Ravens could do a post June 1st release on Chuck Clark, they could possibly trade Chuck Clark, or the Ravens could be like, no, we're gonna keep Chuck Clark. We're making a transition to this new defense. Mike McDonald is somebody who he has been here before, but now he's back and Chuck Clark is known as the smartest guy on this defense. He's the one that calls the plays, that relegates the plays to everybody on the field, gets some guys lined up and whatnot. So why would we take that away from ourselves? Why not just keep him so he can help bring in ushering this new defense? So with Chuck Clark, you know, like Kyle Hamilton is gonna be on the field. He is guaranteed to be on that field. And he's somebody that I think it was after the combine, that's when he started dropping because it's 40, it wasn't so sexy. So since it's 40 wasn't the prettiest, that's when teams, teams like, oh, that's your 40? Oh, forget your real game speed. We're going by 40. Oh yeah, take them out. Oh, you really range you like that in the games?  Yeah, no, we don't want you, let me keep that. That's why it's so important to watch film and not just go by numbers. It's very, very important. And like my God, Josh Hoppin brought out, hey, the Ravens, they, a lot of times they can do pretty well at that to where they don't just go by numbers, but they go by film. Another big example of that was Orlando Brown, Jr. Combine dropped him, dropped his stock. But Ravens saw that, they like, ooh, we got a steal right here. And it worked out, he became a quality starter, pro bowler, multiple pro bowls. And he's still doing this thing over there in Kansas City. But back to Kyle Hamilton. I figure that Chuck Clark now, he's gonna be in the box a lot more. I figure that Chuck Clark may just be at lying back a lot more. Chuck Clark, his role, not even necessarily gonna change, but his usage will. I feel like he won't be dropped back as much. And then they can have Kyle Hamilton in the box too. Like this is going to allow them a lot of flexibility, a lot more flexibility on defense. Now, and this pretty much like guarantees that Brandon Steve, in my opinion, the guarantees that Brandon Stevens is just gonna go back to corner now. Like the Ravens, Marcus Williams, when they signed him, it was like, oh, okay, I figure Brandon Stevens, he'll play a lot of corner this year, maybe some safety too, but he'll play a lot of corner. Since I got Chuck Clark, Marcus Williams, Brandon Steve, but now with them drafting Kyle Hamilton in the first round, oh yeah. Brandon Stevens, he's a corner again in my book. He's a corner again. That's not a bad thing. He's a very physical corner and he's a good tackler. And again, the game, it started slowing down for him a lot last year. But now with Hamilton, good tackler, again, a rangy guy. So all those broken plays, all those deep passes, that should be a thing of the past now. With Marcus Peters and Marlon Humphrey, hopefully they will both be back fully healthy. Marcus Peters is tricky, man. Cause I just, I wonder about his situation with the Ravens. Haven't heard anything about a contract extension and Ravens, I don't know, man. I'm just a little nervous about the business side of things a little bit. Just a little nervous. I don't know. Don't even really want to talk about it. But so Kyle Hamilton, the pick, a lot of people had mixed reviews on it. It wasn't a bad pick though.  It was truly best player available for the Ravens. They like really went by, I know they say it all the time and a lot of teams say that all the time, oh, best player available, BPA, BPA, BPA, blah, blah. But they truly went best player available with Kyle Hamilton. And this can give them a nice tandem of safeties and more athletic safeties with Marcus Williams and Kyle Hamilton for the future. This gives them young athletic guys that can both be moved around. They're not physically limited safeties. They can do more and they can do better. So this, again, it's not a bad pick. It's not a bad pick. And I think once we start seeing him on the field and they get all the boys together, all the secondary together and hopefully everybody will be healthy. I think that's when a lot of people who are very confused by this pick and it's just a head scratcher and it's okay. If you don't agree with the pick, that's fine. I ain't never gonna knock nobody for not agreeing with it because again, y'all, I was confused with it. I was like, oh, okay, okay, that's cool, that's cool. But it sets them up nice for the long run. It really does. It really does. I was just wondering what is gonna be with Chuck Clark, whether they make a move now this year or they just wait till next year. But you know, again, Kyle Hamilton is going to be on that field. He's gonna be on that field.  No, no, no, no. He is going to be on the field and he's gonna be on the field a lot. So just be prepared for that. So great player. And you know, like, man, who's the last safety they selected in the first round? Was it Matt Elam? I feel like it was. But, hey, the secondary could be something special this year again and they still got Andrew Booth out there. He ain't get picked up yet.  So never know, never know, but good move, good move. So, and then again, it's just the first round too. Cause I know a lot of fans are tripping and even though I keep having to remind myself too, hey, it's just the first round, just the first round. Let's see how the Ravens do the rest of this thing, man. Let's see how to do the rest of it. So, they did get some very high quality players, man. So let's see how this, the rest of this thing shakes out. Anyway, appreciate y'all, love y'all. We out.


I think it is important to have someone that you feel is concerned about your well-being and is locked in and tapped into what you need and not the idea of, well, black women are just strong, she'll be fine. Well, we are just strong, but that doesn't mean that we'll be fine. Now, my advice is actually the same for you both. Start with ovarian reserve testing to get a sense of what your egg counts are like. Having a realistic picture of what's going on inside your body will help you both make more informed decisions. Well, I'm not thinking of kids enough to do all that. If I had a nickel for every time a patient changed their mind about family. Like, I'm okay with having a baby at 50. If that is what's supposed to happen, I'm okay with having one at 40. I'm just not interested in trying to preserve right now at 36. If you're 40 years old and you look 20 on the outside, don't think that your ovaries think that you look 20. Like your ovaries are functioning like the ovaries of a 40-year-old, and that is going to be different. Welcome to the Harlem After Show. This is the space where we talk about my favorite topics, the biggest topic from episode three and four of Harlem. Now, if you are not caught up in those episodes yet, don't get me wrong, you can stay. But for the best experience, go over to prime right now. Watch Harlem. There's four episodes of season two out right now, and then come back here. And if you're really behind and you don't know what Harlem is, Harlem was created for people who are eager to celebrate the joy, power, friendships, and range of black women. It stars some people that we have loved for a very long time, and some people that we fell in love with during season one. You can have sex, or you can talk about it.  But this is also not an Ian problem to talk about. This is a Camille just needs to relax problem. Okay, now that we're done with the intros, let me talk to the people, my people, who are caught up on the show. There was so much to love about episodes three and four, like this incredibly satisfying moment. I look kinda like this nigga Drake. It's something about the eyes, the eyes, the nose. Matter of fact, the hair above the eyes. Yep, I mean, to be fair, any scene with Tyler Lepley is a great scene. But my favorite scene by far from the past couple of episodes was definitely the one where Camille and Ty went to see an OBGYN who educated them, and consequently us, on ovarian reserve testing. I didn't know about ovarian reserve testing at all. So, honestly, when you said it, I said, hmm, one of the beautiful things that was not implicitly said, but shared is the power of having a black healthcare practitioner. And that was a beautiful scene to see, also because it was the power of getting a second opinion. Was that powerful for you guys to be a part of that? Well, I knew what you were saying. Yeah, I knew what you were saying. It's interesting, because I was just reading about the young woman who passed away because she was having her second baby. I think she was like 27, and she kept telling them, like, hey, I'm struggling here, you know? And they just didn't believe her, and she passed away. And then, you know, Jerry had made a comment earlier, and she was like, this is the same thing they did to Serena, Williams. If they're not paying her any attention, you can imagine what's happening, you know, all the time, and so I think it is important to have someone that you feel is concerned about your well-being and is locked in and tapped into what you need and not the idea of, you know, well, black women are just strong, she'll be fine. Well, we are just strong, but that doesn't mean that we'll be fine, you know? Which is interesting. I remember I smoked for a few years, and when I quit, like six or seven years ago, I went to the doctor, and I was like, I want to check out everything. I want you to, like, look at every single part of me, and they were like, well, you don't really need that test. I was like, I know, but I want that test. And they were like, yeah, but you don't need it. And I was like, but I want it. And I had to argue with them about getting, like, testing done for just checking if I had cancer, seeing if there was anything that, you know, anything. I just wanted to be preventative and thoughtful about if there is something catching it now and just seeing that. And, I mean, ultimately, I got the test done, but it was like so taboo to them that I would ask for this without having some type of symptom or some type of, like, reason to ask for it, except for that I, you know, did a thing that could cause that. Ooh, sounds like somebody's in the market for freezing some eggs. Um, I don't know if I can have cancer. My number count is low or something. I am joined by my favorite, Dr. Needle Landry, who is the author of my absolute favorite. This actually is my favorite book that I have read this year, for sure. That means so much. This is Crash Course. It is thick, because it needs to be thick. Thick. Can you talk about the work that you do? Well, I'm an OBGYN, so I deliver babies and do gynecological procedures and work in clinics and things like that. But I am actually, I'm a traveling doctor, so I go from place to place, especially marginalized communities. What I love about this book is it is written so conversationally, it is so accessible, and it truly is fit with accessible language.  Absolutely. So what do people need to know about their fertility? People need to know that even if you look 20 years younger than you actually are, you should not make the assumption that your ovaries are functioning the way that they function 20 years before.  Like your ovaries are functioning like the ovaries of a 40-year-old, and that is going to be different. Because as you age, the quality and quantity of your eggs will decline, so you just wanna be mindful of that and make sure that you're planning accordingly so that you have the life that you envision for yourself when it comes to your reproductive future. This doctor was saying that, no, it's 15 to 21 are your peak fertility years. Is that true? A person's peak fertility years will be like late teens to late 20s. So yeah, it definitely is earlier than your 30s because by the time you reach your 30s, your fertility is starting to decline, and that decline becomes more rapid as you enter your mid-30s. And then by the age of 45, the probability of getting pregnant without any type of intervention such as IDF is going to be low for most women. It's interesting because we often rely on our mothers to do these, start these conversations for us, but this technology is really, really new. Yeah, yeah, and I'm assuming you're talking about ovarian reserve testing, right? Yeah, okay, so let's talk a little bit about that if that's okay. Please. All right, what is ovarian reserve testing? Okay, you're born with a certain number of eggs, and that number of eggs is called your ovarian reserve. Well, to put things very broadly and give you a general overview, as you age, two important things will happen. Number one, the quantity of eggs that you have in that reserve will decline, and number two, the quality of eggs that you have in that reserve will also decline, and when I say quality declining, that means an increased risk of things like chromosomal abnormalities, okay? Now, when we do ovarian reserve testing, we're really focusing on issue number one, so we're focusing on the quantity of eggs that you have, and when you do ovarian reserve testing, you're basically asking this question. You're saying, hey, is the number of eggs that I have typical for a woman my age, and if the answer to that question is no, then we say that you have a low ovarian reserve, and that's when you want to definitely have a conversation, preferably with a fertility specialist, just to talk about best next steps. However, if you do have a low ovarian reserve, I also want you to know that that test is just a piece of the puzzle, meaning, hypothetically speaking, you can have a person who has a lower ovarian reserve, but the eggs that they do have are higher quality. The other thing to remember is egg freezing or embryo freezing is a great option to consider, but it's not a guarantee. The only way to guarantee that you will get pregnant and deliver a baby is to get pregnant and deliver babies, but it is a good insurance plan. Now, we're not here to talk about price, but I was looking it up and I thought it was actually cheaper than my brain thought it was going to be. What was your brain thinking? My brain thought tens of thousands and thousands a year to store, but when I researched it was thousands to start the freezing process and hundreds per year to store it. That is accurate, but I mean, that's still a lot of money. It could just be my brain because when people said it, I was like, oh my gosh, it's like 30,000 a year to store these eggs in some high tech clinic. My issue as an OBGYN is I just don't like for people to not have all of the information. So what I don't want is for, like I was having a conversation with a friend who happens to be a little older tech quote unquote a little older, but I was talking to a friend and she was saying, I was talking to my girlfriends and I found out that they froze their eggs. And now by this time she's kind of in the menopause transition. So she's like, I wish I knew that they were freezing their eggs because I would have been interested in being a part of that conversation. So I just don't want anybody to be in a situation where they didn't have the information. They didn't even think about talking to their OBGYN or fertility specialists about the possibility. Because there is a taboo there. Absolutely, absolutely. And the thing about it is a lot of times we just look at social media and we look at the quote unquote highlight reels of a person's life. And not everybody is vocal about having a miscarriage or being or struggling with infertility. And that's okay because they deserve to go to take that journey the way that they want to take that journey. Some people feel comfortable sharing, some people don't and both ways are okay. However, sometimes people, they feel alone and they feel as though they're the only one and they're absolutely not the only one. Along that line of thought, I read a study that said that black women struggle with fibroids more than the average American woman, more than the average white American woman. Is that true and why? That is true. It is true. We don't know exactly what causes fibroids but there seems to be a link to hormones and also there can be a genetic link as well, yes. All right, let's back it up. What is a fibroid? A fibroid is a benign non-cancerous growth in or on the uterus. Now we talked about this offline how in the show the character Ty has fibroids. I was cursed with the Holy Trinity, polyps, fibroids, cysts and apparently I can't do endless transfusions.  Well, their only plan was for me to get a hysterectomy and that seems a bit drastic. Yeah, that doesn't always have to be the first step. Now I haven't been treating you so I'd need to know more about your medical history but there could be a less invasive treatment path before we get to hysterectomy. Why is it important for shows like Harlem to depict conversations with healthcare providers in the way that they did? You need to be able to start the conversation and sometimes you don't know what you don't know. For instance, when she said they recommended a hysterectomy and the doctor said, oh, there are so many things that we can do before that. Well, that's all she needed to say to plant the seed in a viewer's mind that, oh, I have fibroids and my doctor told me I needed a hysterectomy. What else is there? You shouldn't just be jumping straight to hysterectomy if they are clinically stable and they don't have a cancer that requires a hysterectomy. There are so many things that you can do before that and how dare you step in and take that right away from that woman. How dare you step in and tell a woman who maybe might kind of sort of want kids in the future or a woman who definitely wants kids in the future that her only option is to have a hysterectomy. Now, we know that there are other ways to become a mother and all of those ways are beautiful. However, nobody should be telling you that you have to have a hysterectomy if there are other options and I found that that does happen a lot more frequently than people realize. Why is it important for women and specificity black women to seek out a second opinion? It is important to seek out a second opinion because your health is worth fighting for and you have to advocate for yourself and you need to go with your intuition.  This has been proven by numerous studies, even major organizations like the American Medical Association came out and said, you know, this is not conjecture, this is proven and we have to do better. Therefore, taking that into consideration, you need to make sure that you're an advocate for your health and if something doesn't feel right, if you've done research on something and you know that there are other options, you need to seek a second opinion. What is empowering about what you're saying is providing people with the tools and information to rewrite the script but it's also discouraging because they have to rewrite the script. You can't just implicitly trust. So one, I do wanna talk about this because this is an incredible resource for people to get ahead and start asking the right questions and then when they get the answers to check and be like, is that the only answer? Are there better answers or different answers? I wrote that book because I wanted people to have all the information that they needed in one place when it comes to what I call repeat offenders. And when I say repeat offenders, I'm talking about the things that people come to my office complaining about or having issues with over and over and over again. So I wanted people to have a place to go where they can just have the information that they need to ask the questions that will get them the answers they need and deserve in order to be a healthier, happier version of themselves. I love me some Dr. Nita Landry and furthermore, I'm obsessed with Dr. Landry's book. I promoted it before in a couple of videos that truly believe it's a great piece of literature to inform and empower you whether you have to advocate for your healthcare or tell a friend and teach a friend, be the advocate for someone else. Each one teach one is her policy and she lives and breathes that work and I'm grateful for it and if you feel that same gratitude, show it. Go down to the info box, click the link for her book, follow her on social media, you're not gonna regret it and while you're down there, go to the comment section right now and I want you to put anything that you've heard so far whether on Harlem or through the interview I just did with Dr. Landry that you wanna make sure everybody else hears loud and clear and speaking of group discussions. What I love about Harlem actually, it is the perfect show to jumpstart your group chat whether that means asking your friends if they have ever heard of ovarian reserve testing and educating them or starting a debate with people on what's harder, giving head or riding a bike. Both things that I am glad I got the chance to talk about with this beautiful group of people. Have you ever heard of ovarian reserve testing? No. No, and I'm a whole woman. Have you ever thought before about going to get tested or looking into that at all? I am not interested, I don't, I just, I feel like I'm okay with having a baby at 50 if that is what's supposed to happen. I'm okay with having one at 40. I'm just not interested in trying to preserve right now at 36. But do you have an interest in them saying, okay, based on what you have right now, here is what you would need to do to prepare to have it at 50 or here's what you should be aware of. And I say no because I feel like that will change how I approach different sexual situations or relationships. Now maybe I feel pressured to have a baby sooner than I really want to. So now I, mm-mm, mm-mm. I realized, I recently came to epiphany within myself that I wanted to embrace this year as my year of freedom. And, you know, as a woman who's over 35, I felt like the pressures of my biological clock were getting in the way of my dating and my life goals. And this year I decided that I didn't want to do that anymore and I just wanted to be free from pressure, from, you know, society, from family, from expectations, from my, even from myself. And so as a result of that, I'm not putting a lot of energy into the planning of my future children. You're never gonna have more eggs than you have right at this moment. So it's just a bit of information to know, to be like, okay, now that I know that I may have low or I have excessive, what does that information for me and what do I want to do about it? So that actually might be a form of freedom. And so I do plan on freezing my eggs this year. Actually, I'm gonna start the process in a couple of weeks because of that very reason. Because I just want to free myself from the pressure, you know what I mean? And like, oh, if I don't find anybody, dating in LA is bad. I don't wanna think about that anymore. I just want to find my man and then we decide together if kids are for us. But in the meantime, have that insurance of having my eggs frozen for that later pregnancy. All right, with this conversation in mind, let's watch this clip. My number count is low or something.  How are you handling the news? And sometimes we learn legacy is as much about what we leave. I'm not. I don't even know how to tell Ian. I've cost him 68 grand and mirror what I'm just supposed to drop this on him to. Drop what on me? All right, nobody here has had an ovarian reserve test or had their sperm count checked. Correct. You did, in theory, and you found out that you had low sperm count or a low reserve. How soon would you tell romantic partners? After I sit with the news and process my own thing with it then immediately, because those are lifelong decisions. Those are conversations that are very necessary because that could be a deal breaker for him. That might, you know, that might dissuade me from pursuing her further. I might, you know, start looking at other options at that point. And then would you be honest with her with that information? Like, hey, I'm ready, but I know you have to. I'm gonna tell you I would be. I don't know that I would be in the moment.  Yes. Your ovarian reserves are low, so my interest is as well. I don't know that I would do that. Hopefully not like that. I would know I'd be a little bit more tactful. Well, let's talk about Camila Nien. I mean, for the sake of entertainment, it would be so amazing because I love their love story, but I think that if they were real people and they're still instability looming over their relationship, I think that the responsible thing to do or not do is not bring children into that environment. Yeah, it looks cute, but ultimately, I think they would be unsatisfied for sure. And in that clip, you know, that things are looking good and on the up top of them, so it feels like you want them to have that love story, but their past has been kind of messy, right? And then she left him in life. Now we know at this point that he chose to leave his fiance, and this is what happens next, though. Okay, so we finally spent the night together, and it was so different than I remember. I mean, not bad exactly. It's just, I mean, the man has definitely learned some new moves since he been away. Oh, yes! I love when a brother boomerangs back with some age. Toys, bondage, misplay. Literally, who are you?  It's empowering.  Highland's skills. What? Like the cowboy girl. I can't believe I kept the cowboy thing. I was like, oh my God, that's awkward. Yeah. Megan Good, beautiful, oh my God, I have such a girl crush on her. Same. Knowing how awkward she is and how she gets, let's just, we don't have a crush on Megan. I'll say, Megan Good was definitely Megan Good. I was in 9th, 10th grade and it was Megan Good. Same. But her character is very awkward.  So, you know, I think in this scenario of entertainment, I know it gets to her. Would that bother you to have that in your mind?   They will make me go back to the drum boards. Like you're Christmas-y looking at the game tapes. I gotta get right. Because then my question is then, what is keeping him there? You know what I mean? Everything else, your personality, the way that you make the person feel. Sure. Your potential for growing a family together, the business that you guys share, a million other things that make you amazing. We talked about this. Sure. I do not believe that I am my partner as best partner. However, I think what they love about me is my body parts and my minds and my personality and how I make them feel. I'm not the most adventurous.  I'm not doing that. And I don't want to. However, I have this, I feel very confident in my ability to connect with another soul and that's what brings them back. So I think it's really subjective to the experience and, you know, no one experience is the same, you know? I think you could kind of like objectively say who was better at head. 1000% say. For sure. Yes. I experienced a situation. What is it? Is that bad? Snake. Horrible. Are you snaking? Wait, what? I was gonna say, I'm not doing that. Don't do that. I want you to say. I'm not snaking. You like the little motion with the tongue real quick. I've never experienced that. Oh my God. Can we see it? La, la, la, la, la. Like that? That's not bad, the la, la, la, la. But it's the quick darting in and out. Oh, like tongue, like. Wait. I'll get a part of the trick here. You can use your nose to tickle the clit while you lick. Oh. Oh wow. Come on, nose. Tickling the clit with your nose. You know it. Look, if you got a big nose, Mom, what are you doing? That's a fun thing. You might have a quick bit of what you just had. I know it's gonna work. No, no, no, no. You know it. I got a little bit to work with it. So you know, do what you can with it. And I love that there's a little poem there. All right, kind of on this topic right now. I have a question for you. Good. So for us, right, like, vagina to vagina, there's not always a huge difference. I'm sure y'all would say the different. That's not to say the case with dicks. Yes. Right? We know that. Right. Size, girth, length, motion, rhythm. Why does everyone say it's like riding a bike to describe easy shit?  It's like finding a Golden Girls rerun. Those things are easy. Riding a bike is not.    Riding a bike. I'd much rather ride a bike.  I'd much rather ride a bike. Yo, just put your best effort. Just put your best effort. Nah, that's too vague. That's too vague. Put your best effort in. I hold on to what you said and learn how to take direction. So if I tell her, like, yo, spit on that. Yo, grab that. Yo, do that. But I'm very careful in what I say. I liked it, too. I liked it. I enjoyed it. I'm glad you liked it. I'm glad you liked it. I don't listen to it. We'll tell, I don't know if you've experienced it. I've definitely told a woman, like, yo, work teeth a little bit in that five seconds later, the teeth are back. They just remind her. Yes. How many times are we going to remind her? It's just about the technique. The teeth are back. Nobody purposefully scraped her the teeth. It's just an accident. You got teeth in their mouth, sir. What do you want us to do with them? We got gum. Y'all do that when you put your lipstick on.  A riding a bike can get on, you know, you just drive.  Right. OK. Oh, OK, got it. You're doing it. You got it, eh. Don't let go, Dirt. I got you. All right. OK. Other interesting question from the episode. On a scale of 1 to 10, how happy are you? Oh. That's a pivot. That is. That was a question from the episode that rocked her world completely, should correct into simple questions. So. I'm a 9. I'm like 9, yeah. I'm good. I'm in a good space. Manifestation and all that good stuff. Tanisha, I would say I'm a 10. I recently realized that I live this amazing life and very proud of myself and very at peace with myself. I feel like I'm the most healed right now. I feel like I'm not pressuring myself to do or be anything else but myself. And I finally came to that post-35. And I feel like that is the vibe I want to stay on for the rest of my life. So a 10. Right now, I'm a solid 8. I'd say my base, my floor is about a 5. And I'm thinking 1 is miserable, 5 is whatever. It's cool. And 10 is a static. So I'd say my floor is a 5. Right now, I'm about an 8. But I can fluctuate day to day. I'm at a 7. 7, 8. That's heater around there every day. Well, cheers to the fact that we got a couch full of 8s and ups. That's beautiful. That's beautiful.  It is.  It's special and essential for black people to experience joy, especially in this time. But when we do, it liberates others. And it, I guess, expands the narrative on how we can exist and how we can experience love. So, yeah, to me, black joy is liberation. Oh, I love it ahead. That's good.  I hope they felt inspired to do this next. To get, to check on 5 break, because I know there's a lot of people who were like, what is that? You know, as a man, I hear the same things, too. You know, like black women in hospitals, I don't know the math behind it. But you know, we always hear about them just being dismissed and, you know, just being shelfed and, you know, they'll figure it out or she's over exaggerating or whatever the case is.    You know, so it's like it's important for them to see that, for them to also like, you know, have access to that. So even from a man's point of view, it's like that's the important for me to see and reflect it on our show. So by now, you see why we are all so obsessed with Harlem, right? There's so much to cover and we are only halfway through season two, which means that next week on Prime, episode five and six drop on Friday. And then consequently, you're gonna see me back here for episode three of our after show where we go in and discuss all that needs to be discussed. Speaking of which, now is your time to go down to the comments section below. Tell me what stood out to you in episode three and four and let's talk about it.


I consider it privileged to make the statement at the sixth world telecommunication and ICT policy forum where I would want to focus on the key aspect of mobilizing new solutions for connectivity, which is key in unlocking and realizing the ITU Connect 2030 agenda goals. With the advent of the Black Swan event in terms of the COVID-19 pandemic, further realization of the need for universal connectivity as the most critical infrastructure element in enabling the public with ICT solutions has been reaffirmed. Sri Lanka as an example has initiated its own universal service obligation fund project connect Sri Lanka with a bold ambition of enabling Sri Lanka with 100% broadband connectivity across the country, inclusive of all rural and remote areas as well as connecting all state schools with fiber connectivity by 2023. However, the rapidly depleting USO funds would potentially be an impediment and would require a new policy discussion on new avenues of revenue generation for the universal obligation funds of the future. In terms of prioritizing digital inclusivity affordability is yet another significant aspect that needs long term focus and policy considerations were in tandem with the improvement for accessibility through connectivity infrastructure development. Affordable broadband services should be encouraged for achieving an impactful holistic digital inclusivity that would enable to reduce the existing digital divide that is having a negative impact on many demographics for example students lacking access to connectivity and affordable internet restricting education which is a mandatory human right. Sri Lanka today has made a paradigm step by making accessibility free of charge of data costs for all learning platforms of state schools schools and universities and achieving rankings on the top 20 for most affordable broadband services in the future. Let us try to benchmarking report with the new normal creating created through the pandemic rapid adaptation and creation of digital economies, moving ahead from a traditional approach is going to define the future growth trajectory of countries, affecting the quality of the lives of citizens in turn, Sri Lanka's own digital economic strategies based on key aspects of enabling the tech services industry, enablement and empowerment of the local startup ecosystem technology diffusion across non tech industries and capacity building to sustain the thrust of digital transformation which again would be critically dependent on how well we succeed in enabling universal connectivity in terms of accessibility it is equal imperative for us to consider device enablement that would enable citizens to read the digital economies today accessibility to mobile devices has become yet another impediment that must be taken into purview alongside connectivity enablement specially for the student demographic. In terms of creating future digital economies, the device enablement would be key in a adoption of ICT solutions in tandem with focus on enhancing digital literacy and only then we will be able to create a tool inclusive model of enabling digital economies. In terms of time in terms of policy considerations to consider new paradigms of technology concepts such as non geostationary orbit or in GSO systems in accelerating the future of connectivity key aspects of future regulatory landscape changes required for enabling such services would have to be prioritized, ensuring a conducive long term and equitable environment for new challenges by ensuring the recalibration of existing licensing frameworks. In conclusion, I believe that a whole of government approach has to be set in place in achieving digital inclusivity as well as accessibility to connectivity which would ensure that the current digital divide that exists globally will be improved to access acceptable levels, thus ensuring the adoption of ICT services on an equitable note universally. Continuous policy realignment and introduction of policy frameworks will indeed be a catalyst for embracing new technology on a sustainable long term approach which is certain to ensure that we achieve the connect 2030 ITU agenda goals across all countries. Thank you.


Hi, I'm Zor. Welcome to Unizor Education. We introduced the concept of indefinite integral, and now I would like to talk about the properties of this operation. This lecture is part of the advanced course of mathematics for teenagers and high school students. It's presented on unizor.com. I suggest you to watch this lecture from the website, because it has lots and lots of very detailed notes, and for registered students there is a possibility to take exams. Well, actually you can take any number of exams, any number of times each, until you will reach perfection, and the site is free, so basically use it at will. Alright, so properties of indefinite integral. Let me start from something which I said a couple of times before, that integration is an inverse operation to differentiation. So differentiating function we get its derivative, integrating derivative we get the function back. Well, plus constant, if you don't remember, right? Okay, so my first property is the following.  This is derivative of the function, this is original function, plus constant C. Right, it can be expressed slightly differently, and maybe shorter actually. Now, we all remember that this constitutes differential of the function. It's basically like a definition, which means I can rewrite whatever I had on the top as differential of f of x is equal to f of x plus constant. This actually emphasizes even more the concept of differential to be kind of inverse of integral. So we first differentiate function, and then we integrate the function, and we get back the original function. That's the sense in which they are inverse to each other. Okay, fine. Now, this is basically my first property, if you wish, and it seems very trivial right now, but a little bit further when I will introduce another property, it will be obvious that this particular notation has its advantages. Okay, my second property is kind of expected. Integral of constant times function is equal to, oops, you can take the constant outside of integral. How can I prove this? Well, let's just assume that integral of f of x dx is equal to g of x plus C. What does it mean? Well, it means that the derivative of g of x is equal to f of x, right? Now, from this, obviously, we can multiply by a constant. Now, we know that derivative of the product of a function by a constant is equal to constant multiplied by derivative of the function. So this is actually the same as a times g of x derivative. So this is the same as this, right? Derivative of constant times function is equal to constant multiplied by derivative of the function, which means that this thing proves basically this, right? Because derivative of this thing is equal to, now, this is g of x, right? Well, plus constant, but doesn't matter when we differentiate it. So if I will take a derivative of this, it will be derivative of a times g of x, which is the same as a times derivative of g of x, and that's why we have this equality. So basically all these properties of the integrals are proven by the corresponding properties of the derivative. Since derivative of a product function by a constant is equal to constant multiplied by derivative, that's why we basically have this. Because this is, it means this is some kind of function where h of x, where h of x is equal to a times f of x, right? That's on the left side. And on the right side, I have this a times g of x. And derivative of this is also equal to a times f of x. So that's why they're equal. An absolute analogous is another theorem about the sum of two functions. Integral of f of x plus g of x, dx is equal to sum of integrals. How can I do it? Exactly the same way. I differentiate, differentiate of this sum. The derivative of the sum is equal to sum of derivative. The derivative of this thing is f of x, derivative of this thing is g of x, right? So derivative of this is this, which proves the same thing here, right? This means what? It means that there is some kind of a function, derivative of which is equal to, well, I should put, derivative of this is equal to this. So sum of derivatives is equal to this. And derivative of this is equal to exactly the same thing. So they are, but I did not really put plus c in these cases. Let me just say a couple of words about this. When I'm talking about indefinite integral, I'm actually talking about not just one particular function, which is the result of this indefinite integral. I'm talking about the family of functions, which are different, but they are really not very much different. They are different from each other only by a constant. So if this represents family of functions, derivative of which is equal to this, and this represents basically again family of functions, and these are not different more than by a constant and these no more by a constant, that actually makes this equal sign having some kind of a meaning. Okay, the function which is this is different from the representative of this result is different from representative of this result no more than by a constant. That's what basically it means. And that's why I'm kind of skipping the constant because it's obviously irrelevant for all these kind of things. What is relevant is that since the derivative of this is equal to whatever we have under integral there, that's why we can have this particular equality. And next, well, you know what before doing next, let me just give you a couple of examples. We started from this, right? What can be a good example of this? Look at it this way. What is this? Well, this is what is differential of sine. Well, it's a derivative of sine times dx, right? So it's cosine of x times dx. Now we are looking for a function derivative of which is equal to cosine. Now what is this function? Well, obviously it's a sine of x, n plus c. So you see this sine and this sine. This is kind of a demonstration that differentiation is inverse function to integration. Now, another simple case was when I was saying that I can take a multiplier out of the integral. Now, how can I prove this? Well, how can I exemplify this? Let me just give you an example. An example is like this, for instance. Now, on one hand, you can actually just remember, we were talking about the formula. Remember this formula? Why? Because differentiation of this is n plus 1 times x to the power reduced by 1, right? Which is n plus 1 minus 1, which is n. And n plus 1 would be multiplied here. That's why I put it here to get just x to the power of n, right? Now, if you multiply this both sides by n plus 1, you will see this. And you can recognize this as this for n is equal to 4, right? So you can actually very quickly come up with this result. This is x to the power of 5 plus c, right? Because derivative of x to the power of 5 is 5 times x to the power of 4. But let's do it slightly differently. Let's take 5 outside and have integral of just x to the power of 4 using the property which we have proven, right? Now, this thing, 5 times... Now, remember this formula, I was just demonstrating. This is x to the power of 5 divided by 4 plus 1, which is 5, right? Plus c. And this is exactly, again, x to the power of 5, right? So these are simple examples. And now, basically I would say the central example of whatever I was just saying before in today's lecture is integral of some kind of polynomial. And as a polynomial, I will take something like 4x to the power of 3, 3x to the 2, 2 to the x plus 1 dx. Now, since this is a sum, integral of sum is equal to sum of integrals, and each one of them has a multiplier, so I can take it outside of the integration. So it would be 4 integral of x to the power of 3 plus 3 integral of x to the power of 2 plus 2 integral of x dx plus 1 and integral of dx, right? Which is equal to... Well, this is x to the power of 3 and integral of that is x to the power of 4 divided by 4 and 4 and 4 will cancel out, so that would be x to the power of 4. Oops. x to the power of 4. Now, this would be obviously x to the power of 3 divided by 3 and multiplied by 3, so it would be x plus 3. And this would be x to the power of 2 divided by 2 and multiplied by 2, so that's 2. This would be an integral of 1, which is x plus constant c. So we have used right now all these basic properties, the linear properties, if you wish, which means you can multiply by a constant and add under integral expression and spread it over multiple integrals and take each one of them separately. Now, if it's a little bit more complicated function, but also which can be separated into pieces, something like this, you still can consider this as sum. Integral of this is x to the power of 4. Integral of logarithm, well, we don't know yet, but anyway it's easier than to integrate the whole expression. And later on in today's lecture I will explain how to find integral of logarithm. But in any case, that's easier than this. So this linearity of indefinite integral is a very, very basic fundamental property which is very, very important. Now we will do something a little bit more difficult. Well, you remember that derivative also is kind of a linear operator. The multiplier by constant can be brought out of the derivative. The derivative of sum of two functions can be separated into sum of derivatives. So these are linear properties. Now, what about multiplication? Hope you remember this function. If you want to derive, to have to take derivative of this, remember the formula? So that's not basically as easy as sum of two functions, right? The product of functions, of two functions, derivative of this is a little bit more complicated than the product of derivative. So it's not product of derivatives. Just remember this. Now, same thing with integrals. However, using this, we can find some very helpful formula for integration. And here is the formula. Let's integrate both of these. Now, integral of this, integral of derivative of the function, function being the product of these two, is the function itself. We talked about this as the first property. So integral of this is f of x times g of x, plus constant, okay? But let's just forget about this constant for a while. We assume that we know this. Now, on the right side, if we will integrate, that's the sum, right? So we can do it as a sum. Okay. Now, this is basically a straight consequence of the formula for derivative, right? What's really very important here, that integral of sum is equal to sum of two integrals. That's what I was using, because integral is a linear function of the function, linear operator, I should really say. And this integral of this is integral of derivative is equal to the original function from which we started, right? Because what is integral? It's a function derivative of which equal whatever you have here. And we already have a derivative, right? So that's what it is. Now, from this, we can derive a very helpful formula. Formula basically is very simple. We just resolve it for one of these. For instance, we have something like f of x times derivative of the function. Then what we can say is, we can say from this, it's equal to product of the functions minus integral, and we will reverse the integration here. Oh, sorry. GFX. Now, this is a formula which is called integration by parts. Well, I don't know why they called it this way, but anyway, that's the official name for this integration. What is important is to realize that this is not just any function. So we are not talking about integral of a product of two functions. We are talking about integral of the product of any function and derivative of any other function. Then in this case, we can actually change it into this. Now, why do we have to do this? This looks simpler than that. Well, it depends. It depends on what is the function f and what is the function g. And you will see in a couple of minutes that in some cases, it's much easier to deal with this than with this. So it all depends. If function f is kind of simpler, whatever, and especially it's simplified when we are getting a derivative from it, then it makes sense to do it this way. Now, which functions are simplified by taking derivative? Well, obviously, the power function, right, x to the power of n is some multiplier and then x to the power of n minus 1. So we are reducing the power by differentiation. So this might be a case when function f of x is some kind of a power of x and this allows us to reduce this power. So that's basically the reason. But you will see the example of this. Okay, now, let me just give you an example of this. Integral of x squared times e to the power of x dx. Well, obviously immediately you don't know what is the function derivative of which is this. So you can use this rule f being x squared, g being e to the power of x and derivative of g of x, derivative of e to the power of x is e to the power of x. We know that, right? So this e to the power of x is both g and g of x, which means that I can use this one, which is x squared times e to the power of x minus integral of this. Now, what is derivative of x squared? That's 2x, right? So it's 2 outside of integral x and the g is still e to the power of x. This is exactly what I was just talking about. This is simpler because this is the first power and this is the second power. First is simpler. Now, this is not the end of it. Now I don't know what this is, but I can do exactly the same thing again, right? So I have my x squared e to the power of x minus 2 and this integral I will also represent in this way x being f of x and e to the power of x is g of x. So it will be what? x times e to the power of x minus integral e to the power of x times derivative of x is 1 dx. Now, this is, again, simpler. So what's the result? The result is x squared e to the power of x minus 2x e to the power of x plus 2... Now, what is integral of e to the power of x? Well, e to the power of x is the function which has a derivative equal to itself. So that will be e to the power of x. Derivative of e to the power of x is e to the power of x. That's why integral is equal to exactly the same, plus c. And that's the answer.  And that's the result. This is the result of integration. Now, I wiped out my main integration formula. So it was integral f of x g of x dx is equal to f of x g of x minus integral of f derivative g of x dx. Let me see if I can change my marker. Okay, now, let me slightly modify this. It will be a little bit shorter. You remember that g derivative times dx is basically a differential of f of x, right? Of g of x. So I can rewrite it as following. f of x dg of x is equal to f of x g of x minus integral. Now, this is g of x times differential of f, right? So this is basically another representation of exactly the same thing. I'm just combining g derivative times dx with differential of g and f derivative times dx as a differential of f, right? And that is a little bit more common representation of integration by parts. And let me just give you an example of this. For instance, I actually don't need this and I don't need this. It already played its role and I have more real estate. Now, for instance, we have integral of x square d sine of x. And again, remember this x square. If I will replace differential of sine with differential of x square, I will reduce the power by one and then I can do it another time. So this is a typical thing. So this is my f. This is my g. So it's x square times sine of x minus integral of sine of x d of x square, right? Now, what is differential of x square? Well, that's a derivative times dx, right? The derivative of x square is 2x times, so it's x square sine x minus 2 sine x times x times dx, right? And here I will do exactly the same thing. x square sine of x minus 2. I will combine sine of x and dx into differential of cosine, right? Actually, I need this minus because derivative of cosine is minus sine, which is minus sine and dx. So that's how I did it. Now, this, again, I will do exactly the same thing as before. I will integrate it by parts. So I have x square sine x plus 2. So it's f times g, x times cosine x minus integral cosine x dx, right? Cosine and differential of this function. So in this case, when I'm using differentials, it's kind of more symmetrical, equals 2. All I have to do is to find integral of cosine. Now, I know that the derivative of the sine is cosine, right? So this is basically my sine. And my result is plus 2x cosine x minus 2 sine x plus constant c. So that's the result of my integration, okay? So this function has integral, which is this. And as a consequence of this, I have a very simple case when I can integrate the logarithm, which I promised in the beginning. So how can I integrate logarithm? Well, I don't know any function, elementary function, which has a derivative equal to logarithm, right? But here's what I can do. Now, this would be my f of x and this would be my g of x. Plain x is also a function, right? g of x is equal to x and f of x is equal to logarithm x. So integral is equal to product of the functions, which is x times logarithm x minus. And now I will change whatever was a function becomes differential, whatever was differential becomes a function, right? So x times differential of logarithm x equals... Now, what is differential of logarithm? That's the derivative times gx, right? Derivative of logarithm is 1 over x, right? Well, obviously we are talking about logarithm, which means we are talking about only positive values of x. So we can reduce it and I will have just 1. And integral of 1 is what? It's just plain x, right? Because derivative of x is 1 and constant c. So this is integral of logarithm. And we have derived it using this integration by parts. Very important, actually. Obviously we have to know when to use it because sometimes we can actually use it and we get more complicated results. After applying this rule of integration by parts. But in some cases, like in this one or when this function is some kind of a polynomial, for instance, it helps. Because then when we differentiate it, it will reduce the power. And by the way, differentiation of logarithm is also kind of simplifying our story. Because logarithm is a little bit more complex function versus 1 over x, the derivative of x, which seems to be a little simpler, right? Alright, so these are basic properties. Now, they are linear properties, like constant multiplier or sum, which are really very simple and trivial. And this more complicated property of integration by parts, which is very much used in many, many different cases. I do suggest you to look at the notes to this lecture on unizord.com. The notes presents basically only the basic points of this lecture and exercises, which I have just done with you. Try to do these exercises yourself and see if you will receive the same results as I did. Alright, that's it. Thank you very much and good luck.