It's the same old story that it's always been, Dr. Elaine Wick said. The farmers and ranchers keep slashing and burning their way into the forest. When they encounter local tribes, they drive them off, sometimes by force. There are supposed to be laws in place to protect them, but the local governments are less than eager to enforce them. If you could put a word in with your superiors, I'll pass your concerns onto them. The man known as Joseph Knight said. But I can't guarantee that they'll take action. I'm only here to assess the historical significance of the find. Of course, that's what UNESCO needs to be concerned with, Dr. Wick said bitterly. Protecting the ruins. Those have world significance, don't they? The United Nations is, of course, concerned with the human rights of the indigenous inhabitants, Knight replied. But that doesn't fall under my jurisdiction. I can promise, however, that your concerns will be passed on to the relevant authorities. That's all I ask, Dr. Wick said. The Yashua are a fascinating tribe and it would be a crime if their culture and heritage were destroyed so that Americans can get fat on hamburgers. I prefer tacos, Knight said. If you'd excuse me, ma'am. He nodded respectfully to the doctor and walked out of his trailer into the stifling heat of the Amazon rainforest. His thin shirt clung to his body and the chirping sounds of insects and brightly colored birds surrounded him like a kaleidoscope of sound. The camp was a small one. Several tents, a latrine and a trailer with computers, satellite uplinked and a gasoline powered generator, augmented by solar panels. The structures were arranged in a loose semi-circle at the base of a massive temple, hundreds of meters tall, made of hand-cut stone, covered in crumbling reliefs and tangled masses of vines. Thirteen archaeologists and anthropologists had come to this place to study the so-called Yashua pyramid, already being hailed as one of the biggest archaeological finds of the century. Mr. Knight and a few other members of the team were here for a different reason. He saw James Zhao wave to him and nodded to the young Chinese-American man before jogging over next to his colleague. Can you confirm? He asked. Not yet, Zhao said brimly. I'm still trying to figure out what's going on here.  I've convinced the teams that we need to catalog and study the exterior in depth before we even think about entering the structure, Zhao said. It's only a matter of time before one of them slips their leash and tries to open up one of those doors. I can't exactly tell them not to open up King Tut's tomb, can I? Do your best, Knight-Side. Seriously. Try hard. The council was adamant on this point. Whatever's inside here, it caused half of their oracles to have a foaming fit when the discovery was announced. We cannot let this place get opened until we figure out what's inside, if someone does and something bad happens.  The murderous, marauding, savages thing doesn't really go over well these days. Besides, they seem like nice people. Speak of the devil, Zhao-Side. On the other side of the camp, a slight, rangy man with leathery, caramel-colored skin was walking towards them. He carried an ornately decorated blowgun come spear come walking stick in one hand and his shirtless body was covered in ornate interlocking tattoos. Out of respect for the newcomers, the man had traded in his traditional garments of woven plant fibers for a pair of brightly colored shorts. He had also traded in his traditional hand-woven sandals for a pair of leather Birkenstocks. That had less to do with respect and more to do with comfort. Yeshua's shoes were notoriously uncomfortable. Mr. Tashika, Knight said, inclining his head respectfully. It's good to see you again. And you, Mr. Knight, the man said. His English was tinged with a low, guttural accent. The Yeshua language was largely glottal. Your studies go well? They do indeed. We've been studying the bash reliefs on the walls of the pyramid, Knight said. They're fascinating. Do you know anything about them? Tashika laughed out loud and shook his head. I wish I could tell you that this was an ancient holy site to my people and maybe even quote you some ancient story passed down from mother to daughter for countless generations.  The Yeshua never came here often. There's no river here. The soil is bad and the hunting poor, which is the interesting thing to me, Knight mused. People don't often build huge buildings out in the middle of nowhere. Buildings this big usually get built with some kind of natural resource to draw upon. A river for trade or fishing. Fertile ground for farming. High ground for defense and isolation. Not to mention that you don't often find temples without ancillary buildings around them. Ancillary? Secondary? Knight clarified. Things like homes for the priests or farms to feed them or to house craftsmen or merchants. Those almost always pop up around religious centers like temples. It's not often that you see a single building like this out in the middle of the jungle. Then maybe this isn't the temple. Tashika suggested. Knight paused for a moment, carefully choosing his next words before going on. There's really nothing else it can be, he said, trying to keep his voice calm. Tashika was treading dangerously close to the truth here. A building this big? What can it be? I do not know, Tashika said, but he left nervously and rubbed the back of his head.   Just go on and tell me. Alright, the actual man said, sighing, look, our village has this, this old woman. Crazy old crone. We call her the great mother. They say that she can see the future. It's all ancient legends and myths, but it's part of our culture.  Yeah, Knight said, shamans and wise women are universal. He vaguely remembered meeting the old woman, when he and the UNESCO team had made their introductions to the local Yashua tribes. He remembered a withered old woman with one arm, leaning heavily on a stick, glaring angrily at the interlopers into her village. He also remembered Jiang telling him that the woman's eave signature was showing distinct tendencies towards extrasensory perceptive abilities.  That's a 30 mile journey through the jungle. I don't usually make that journey until a few months later in the year. But she's insisting the disaster is going to befall us if we remain here. And she's got my father so riled up that he's agreed to move the tribe early this year, that she can laugh nervously, hiding his teeth with one hand. It's all tribalist bullshit, but the older folks are taking it seriously. What looks like I won't be able to help you guys out anymore. That's a shame, Knight said and meant it. Tachica had been a treasure. A Yashua man raised in the culture of the tribes, but raised in the city and college educated to boot. He had been invaluable in smoothing out negotiations between the UNESCO team and the Yashua. And Knight was certain that he was going to miss the young man. Maybe when you come back to your summer grounds, you and I can meet up again. If you are still here, Tachica agreed. It may be that you'll find out all you need to know about this place before then and you will go home. Perhaps Knight agreed. I'll go let the others know, Tachica said. Thank you for your help and for your respect, Mr Knight. Good day, Mr Zhao. Tachica, Zhao said, extending his hand in friendship. Good luck, I'm going to miss you. And I you, Mr Zhao. The young man inclined his head respectfully to Knight, then walked away to say his goodbyes to his friends on the rest of the UNESCO research team. Knight shook his head, brow furrowed in worry. Jimmy, why does an old proverb about rats and sinking ships come to mind? I was thinking the exact same thing Zhao admitted. Mr Knight, Knight awoke slowly to find Zhao leaning over his cot. The young man's face was drawn with worry. After Knight, Zhao said, I think it's happened. What's going on? Knight asked, suddenly alert, Timothy and Jonas are missing. And one of the temple doors is open.  I don't think it's their fault, you'd better come see. Knight understood the moment that he came out of his tent. It wasn't hard to miss the knocked over tent on the edge of the camp. Highline snapped, steel poles bent in two. One of the nylon walls had been shredded, as if by some massive claw. There was a dark blotch on the ground that looked a lot like blood. Who else knows, Knight asked. Two other researchers, Lin and Tamaki, I think that's it. Alright, Knight said coldly, you talk to them, get them to keep quiet. Tell them it's a bear or something and we're going after them. I'll get the gear. Knight strode quickly across the camp to the equipment tent where he unlocked a box of gear that he had kept sealed since arriving in South America. Inside there were two headsets, a pair of M4 carbines, ammunition and a satellite phone. He took out the rifles first, checked to make sure that the chambers were empty and put them aside. Knight then picked up the satellite phone and dialed a number that didn't exist in any phone directory on Earth. Central, a soft feminine voice said. Report. Central, this is Tasker 1, Knight said. Authentication code VictorAsagai922. Tasker 1, Central confirms, bringing up your case file now. Transferring you to your appropriate controller. Wait one please. Knight picked up one of the two headsets, checking out the Oculus Riggs batteries and doing a quick diagnostic while journey's wheel in the sky played over the phone. The phone picked up before the song had a chance to repeat once. Tasker 1, this is Central Authority. Report over. Central Tasker 1, I've got two missing civilians and the temple doors have opened. I'm about to enter the structure with Tasker 2. Third mission priority, I am escalating to response level 3. If you don't hear back from us within three hours, consider it a response level 4 emergency. Please confirm. Over. Tasker 1. Central confirms two missing civilians, temple doors open. Central confirms your escalation to response level 3. Central will escalate to response level 4 at 0600 hours, local time. Over. Thank you, Central. Tasker 1 out. Knight hung up the satellite phone and hung the unit from his belt buckle. He picked up an empty day pack and packed in food, water, medical supplies, and a laptop computer. Zhao joined him in the tent shortly after, and Knight helped him to pack a day pack of his own. The two men emerged from the tent, carrying their assault rifles and wearing their night vision goggles. He could see two of the researchers from the UNESCO Archeology team standing by the tents. Lin raised her eyebrow in alarm at seeing the two men dressed like special operations soldiers. Alright, Knight said shortly, we've got two missing personnel, possibly kidnapped. Zhao and I are going to see if we can get them back. Lin, if you don't hear back from us by 0600, sorry, 6 o'clock, take everyone, pack them into the vehicles, and drive towards town. Find the nearest American embassy and tell them what happened. What did happen? The hapless Lin exclaimed, I don't get this at all. Terrorists, Knight said grimly. I think they kidnapped Tim and Jonas. I'm going to see if we can't find them.  You need to make sure the team gets to safety. You're in charge here. Lin hesitated to say more. Then finally, just nodded, be safe, she said, terrorists, huh? Zhao whispered as the two men started jogging towards the temple. The catch-all escalation for all weird-ass activity, Knight agreed. Through veritas, the interior of the abandoned temple seemed to glow with a sickly greenish light, the patterns vaguely resembling those of blood spatters, or nails being raked across stone. Greenish mist seemed to swirl around the two men, raising goosebumps on their bare arms. The image of a flayed skull raced towards Knight, lipless, mouth open, in a wordless scream, then vanished into the darkness. Bad things happened in here, Zhao whispered. Very bad, Knight agreed. It took a lot of emotional and spiritual violence, for Eve's signals to linger as deeply as these did. There had been murder done in this place, and worse, Knight, Zhao said softly. He gestured to a spot on the ground that had a brighter veritas signature than the others. Knight dropped one knee and ran his hand over the pool of brightly shining white light. His fingertips came away sticky. He put his fingertips to his nose and smelled blood. It's fresh, he said, couldn't have been shed more than a few minutes ago. I think we're catching up to them. It was then that Knight heard the moaning. It was very soft and very low, no louder than a kitten's cry, but it was low and guttural and tinged with a nasty, wet sound. It was coming from deeper into the temple, further into the darkness. You know, Zhao quipped. It's at this point in all the horror movies that I always started yelling at the girl not to go into the dark, scary temple. Just go home. Who cares what's in there? Yeah, Knight agreed. But he raised the rifle to his shoulder and continued to walk down the dark, mildewy hallways, closer to the sound. The light was dim. It was the color of fireflies, thousands of them. It flickered and glowed dimly, up ahead in the dark. Knight stepped into the central chamber and he felt his gorge rise. The thing in the center was a massive matter about knee high. It was spongy, laced with tiny holes about the width of a pencil. Thousands of small glowing maggots rise and borrow their way through the mass. Their tiny bodies inching forward bit by bit, slowly but surely. The thing on the top of the mass wasn't Jonas, not anymore. Its eyes were frozen open in terror, its mouth wide open in shock. One of the maggots was eating its way out of his lower lip, as three more borrowed their way into his left eye. His hand was outstretched towards Knight.  Knight reached out with his weapon and gently poked at Jonas's hand. It indented slightly under the touch, leaving behind an impression of the rifle's muzzle, like wax. Soap, Zhao whispered. They're turning into soap. God damn, Knight whispered. He studied the mass a little closer. There huddled up next to Jonas. His arm and torso melting into the other man's was Timothy. All right, Knight said. We're out of here. Seal the door. Get the UNESCO team out of here. Call in strike. This is way above our. Sir, a soft female voice said behind them. Mr. Knight? Knight spun around, rifle raised, to find Lin standing behind them. Mr. Knight, Lin said. I left to Maki in charge. He's getting everyone ready to move. I thought you could use the help. Oh my. Zhao grabbed the young Chinese woman before she could scream, slapped his gloved hand over her mouth and held her down while she struggled. Something moved inside the glowing chamber. And Knight spun around to see maggots, glowing ones, thousands of them, bursting from the mass of soapy, waxy material that had once been Jonas and Tim.  And Knight turned to Lin and Zhao and screamed for them to run as his feet turned towards the exit and he bolted for his life. He heard Zhao scream as the things caught up to him and Lin. Heard Lin start to shriek a moment later. Then he felt his ankles give way and he collapsed to the floor, banging his chin hard against the stone and seeing stars. Knight spun around, rifle raised. The glowing green tide was wrapped around his ankles, dragging him towards that massive soap and wax and horror in the center of the chamber. Lin and Zhao were already in it, already starting to melt, already starting to have those horrid green maggots crawl in and out of what had once been flesh and was now closer to soft cheese. His left arm was already crawling with the maggots. He had to drop his rifle to pull off his day pack and unzip it. He grabbed a laptop computer and held it to his chest tightly. His eyes were gone, already eaten by those crawling worms. He had to find the power switch by feel. Hold it down for five seconds with the computer screen closed. He was already dead when the bomb exploded.   What had once been an ornate stone temple was now a crater in the ground. Three hours had passed since Central had awoken strike team broken dagger and abortated them into the South American jungle. Now, as the 12 members of the strike team advanced towards what should have been an ancient archeological site, all they could see was a wide crater filled with glassy rubble in the middle of the rainforest. Ever seen something like this before Jackal? She asked her ex-o as the rest of the team split up to search for survivors.  Ma'am, Arsageik said over the comms, I think I found something. On my way, Fox said. She got back to her feet and jogged over to where the other soldier was looking down at something in the tall grass. It was a pair of Arco's headsets, glowing softly. Their visual components and visor melted and burned, but there were quarters intact. The two items were laying on a patch of grass in which a complex geometric form had been burned, reducing the plant life to white ash. Emergency dump, Jackal said. Someone hit the panic button. Bag it, Fox said. I'll report this in. Arsageik pulled an evidence bag from his thigh pocket and gingerly picked up the two black boxes, dropping them into the Mylar container and sealing it with double-sided tape. His Oculus visor would record the location and the time of discovery, but he jotted down a quick note on the outside of the bag in permanent marker, none less. So what was this, Jackal asked? A failed mission or a successful one? Fox didn't have an answer for him. She still couldn't decide how to answer that 12 hours later when the helicopters came to take them home. End of file. To learn more about the SCP Foundation, subscribe to SCP orientation today and turn the notification bell on so you don't miss any of our videos.


My name is Richard Marbs. I'm an Air Force veteran. I was injured in a flight-line accident. My leg was damaged. I was about to turn 20. Yeah, I was pretty young. And they diagnosed me with osteosarcoma, which is a pretty nasty form of bone cancer. So I was sent back to the state stand for my surgery. We had 60 amputees on the ward that I was on. There was a real bonding there because of our age, I think, which also helped us all to get through the stuff. I wanted a job and I couldn't get one. And so then I went to school alone. It was okay. But so I was so glad when I got a job. To me that was a victory. Getting employment and becoming financially independent. And then I could start thinking like I had before. I'm a veteran and my victory is coming back home and finding a job and living a normal life.


Can you guys hear me? Hello? You listen? OK, that's working. So welcome. Thank you, everybody, for coming. So my name is Rafael Rosa. I work for the internet app. And today I'm going to talk about our cloud product, which is using OpenStack. So just a sec. OK, one more time. Sorry. Wrongs I said. So I work for internet app and iWeb. We are a hosting company, an internet service company. We provide infrastructure services like co-location, hosting, and cloud and network, network services like CDN, IP, high performance IP, and other things like that. So we are hosting more than 13,000 clients on data centers spread around the world. And we have data centers in North America, in Europe, in Asia, and we have more than 750 employees. In December 2013, internet bot iWeb, which is a Canadian company. And that's where I'm from. And so that's it. I'll show you briefly what do we provide as products. So our portfolio is quite big, and it's focused on two main things, performance and flexibility. We provide all those products, like cloud, bare metal, dedicated server, and co-location, and allow our clients to use them in conjunction. So you can have, for example, bare metal server and co-location systems and make them work together. And the same goes for cloud. All of this is provided with accelerated networking that we have from our Pops management services in a single control panel that you can use to manage everything. So these are the places where we have data centers. The ones in green are the ones that are managed by internet, owned and operated by internet. The ones in blue are the ones that we have partners around the world, and we are always expanding our network. So we're mostly concentrated in North America, but we are expanding. But how did we get here? How did we get to the point that we're talking about OpenStack? So in the beginning, the internet and our web were pretty much a traditional hosting company. So we offered hosting, co-location, network services. That's what everybody does. That's very traditional. And then came a time when the cloud became a thing, the future, the future of hosting is the cloud. And we decided to take a leap and provide a new product that is going to take advantage of all the cloud things like self-serve purchases, sorry, API, paper use, and other things. So to do that, we chose to use OpenStack. OpenStack is a good platform for what we want to do. It's created by the brightest people that we have, a big community, a welcoming community, a community that wants to share knowledge. And that's very good for us. We don't need to reinvent the wheel every time that we want to create a new system or we want to provide a new service. We can use the expertise of this community to help us provide a better product for our clients. And back in 2010, that's when we started looking at OpenStack. So we already had some commits done in Baxar. So since Baxar, we are already contributing code. And we are trying to work with the community to provide a better OpenStack for everybody and trying to improve the ecosystem for everybody. So here is a brief summary of all the contributions that we made. We had a lot of contributions, also during the Havana Grizzly period. And during this time, we had lots of contributions for Cinder, for example. We use SolidFire, and we provide a lot of help to create the Cinder driver for SolidFire. And we committed code for that. And we also helped a lot with the Stack Forge project, which is the puppet automation for installation of OpenStacks. One of our contributors, by the way, is Macheganier. Perhaps you guys have seen him during the videos that were shown today during the keynotes. He was elected super user because of his contributions, both on code and also as a reviewer. So we are very proud of the contributions that internet and I web made to the OpenStack project. So OK, this is how we got to use OpenStack. This is how we interact with the community. But how do we make OpenStack something that is unique, that is different from what we have on the market, that's better for our clients. And it provides the values that we see on the internet. We decided to get OpenStack and change a little bit how we deploy it. We chose the right stack for the job. In this case, we decided to use an all SSD storage solution because we want to have the best performance for our clients. So we offer two different kinds of flavors. You can have ephemeral storage with instance SSDs, or you can have persistent storage using solid fire. On both situations, you're using SSDs. And we're providing the best performance that we can on the storage side. The other thing that is very important for our clients is performance guarantees. Our clients come to us because they want the best performance. They don't want to suffer from issues like noisy neighbors or paying for performance that they're not getting. So how do we do that? We created different flavors that provide guaranteed CPU threads for each one of those clients. And we don't oversell the CPU for those flavors. And that allows the clients to use full thread of CPU when they choose those flavors. On the storage side, we provide iOS, QOS, on IOPS, on solid fire. For each volume that you create, you can set up how many IOPS that specific volume can use. And that way, we guarantee that the client will have access to the performance in the storage IO that he needs when the time comes. Another thing that's coming soon is that we're going to provide, through the same API and through the same control panel, bare metal flavors running on OpenStack. So instead of creating a VM, you'll be able to instantiate a bare metal machine that will be provisioned in a couple minutes. And you have the full VM for you, no sharing.  And for some clients, that's very important because you can extract all the performance that you need from the single machine. Another thing that we did, and it's very important for us, is how can we deliver the best networking experience for our clients? We do that by improving the network and creating cross-platform setups. So what happens is, as I mentioned, you can have machines running on our OpenStack cloud. And then you can have other different servers, like database servers, running on bare metal machines on the hosting side. Or you can even have legacy infrastructure running on colocation. And you want all those things connected. You can do that through our networks. You create those machines, connect to them, and you have a private network that you can use to transfer data across all those infrastructures. This allows you to choose the right infrastructure for each job. And we also use our mirror technology that provides the best. It provides the low latency connection by choosing which ISPs it should use for each client on a real-time basis. On top of all this, you have a single pane of glass that is a single one place that you can manage all those resources with the same features, with the same UI, and with the same support. And that's very easy for users because they don't need to learn two different tools to use our infrastructure services. So in the end, what we were able to create is an evolution. We can allow clients to move from the cloud to colocation and vice versa, depending on their needs. So let's say that you have small deployments, or you have elastic workloads, or you create a new infrastructure. All of these is much easier to do if you're using the cloud. You don't need to think about it. It's very easy. Click, click, click. In five clicks, you'll have it working. It's a little bit more complicated if you need bare metal. But we allow them to evolve. After some time, perhaps, you need more performance, or you need dedicated servers. We allow you to add those servers as you need and take advantage of them and go up to colocation. That's very good for people moving legacy workloads that are running on old machines, but they want to use the cloud. And they don't need to choose one or another. They can mix them as they need. I'll use a couple of clients that we have using our OpenStack platform to showcase how flexible it is. So the first one is Carl Jr. This is a very interesting case. He's a 17-year-old guy that is a pro gamer. He is the world champion of Trackmania 2 Stagen on the Electronic Sports World Cup. So this is a 17-year-old kid that used the cloud to create servers so he can train with his friends and alone. This guy trains six hours, eight hours, doing this racing game every day when he's training for competitions. And he uses the cloud. He's a very small user. One cloud is good enough for him. We allow him to do that on our cloud. That's the card that he uses sometimes when he's playing on games that are sponsored by iWeb. Another use case, which is much bigger and very interesting is Cortica. Cortica provides real-time image recognition software that can be used, for example, to recognize a picture and choose the best ad that goes with that picture. Imagine that your clients are uploading a picture of a beach. So their software can recognize that and then provide, for example, the best travel ads based on the picture without anybody needing to add meta tags to that picture. And that's very cool. It's automated. Everything's automated, and it uses a lot of resources. They use machine learning to accomplish that. And most of the times, they use bare metal machines to do this because that's the best cost benefit for their use case. But the thing is, they also use the cloud for POCs and dev and test. So we give them the flexibility of using the cloud to access their bare metal machines and make their systems work. And they don't need to choose. They are choosing the best tool for the job. The last case is Boink. Boink is a company that provides unlimited music streaming and downloads for mobile apps in Venezuela and Chile. So they provide this limited streaming, and they are hosted with us. And they use all our products. They use a bit of cloud. They use a bit of hosting. They use a bit of colocation. And they use our networking services as CDN. So they use CDN to deliver the media to their clients. They use the cloud for some tests and dev and for some elastic workloads that they can spin up and down when they need. They use hosting and hosting for their media, for their media storage. And they use colocation as DR and also other types of media storage. So they use all the services together and they can deliver the best solution for their clients. They can deliver the best performance for their clients and they can use the right tool for the job. It's always the right tool for the job. Our main focus is delivering performance and flexibility, right? So today we announced the next Generation Agile cloud that is GA today. It's running on OpenStack Havana. You can have access for our site. You can use the API to provision new machines. Just go up and sign up. As we told you, it's all SSD-based. The network is designed to work in hybrid environments.  Be them cloud products, bare metal or colocation. So that's what I had. Thank you very much for coming. If you want more information, please visit us at booth D7. We'll be there to provide more info and to clarify any questions. Thank you.


There's another way that we can use to look at the volume of a cylinder First of all we we are using double integrals, and we're just using the xy coordinate Cartesian coordinate system We can convert that to a polar grid If we do the conversion to the polar grid it might be easier for us to do this remember we were still using the fact that z equals the f of some vector function or of x and y equals some constant h So we have this cylinder going up to a flat plane and we want to denote We want to get to an equation for this of volume using just double integrals now instead of using then the fact that we have a type 1 region going from this y equals 0 up until this y equals the square root of a squared minus x squared Where we have the fact that this outer cylinder the outer wall of the cylinders x squared plus y squared equals some radius called a squared So this whole radius here would be till a Now the same as we did with normal Let's do it this way remember we are doing our double integral over some region at the bottom Let's call it region R our function is just a constant over some area and Because of the type 1 region we call da equals dy dx That is how we made these infant tests to some really small little Blocks and we sum over all of them that is an integral But now we're going to construct a different tiny little rectangle block and here I have to note to them. We've scaled it up in as much as we have this tiny little angle d theta and This tiny little angle d theta can denote if it's very small it approximates the width of this little rectangle of us of ours and If we look on this going from zero till the radius going from zero till a we have a here If we take just an infinitely small part of that and we call that DR If we call that DR, that'll be the height of our little rectangle Now we just need the width of our rectangle and what is the equation for and for arc length? remember arc length Equals just the radius times The little angle that you the angle that you meeting theta 2 minus theta 1 equals delta theta That is certainly what we are going for So that is arc length and if it becomes infinitesimally small this approximates a straight line So we still have height times width So what would be this area?   That's what we did with the Riemann sums when we started learning about integration We're still constructing these tiny little areas.  So For Cartesian coordinate system, it was this x times y dy dx So now we have our dr d theta. So let's just work out what the bounds are going to be we'll take conventionally. We'll put the R In the middle because it usually is a constant now. What happens to the radius it goes from a radius of zero to the radius of a So that becomes easy the inner integral here The inner integral becomes very easy In as much as as far as h. There's a r dr the dr becomes From zero till a and on the outside. We just have to think what happens to this angle theta Well, we're going from theta equals zero all the way around to two pi That's what's happening. We're sweeping this tiny little blocks all the way around and all the way from the center out and if we add then all these Uncountable little rectangles we are integrating so that goes from zero to two pi and that is going to be the volume of this cylinder of ours between this plane at the bottom and a y-axis which we haven't drawn here Equaling z equals h or the f of x and y equals h And there we have it with a d theta So this is going to equal zero to two pi. We can take the h out Going from zero to a of r dr, and then the outside function d theta From zero to two pi of h. What is this? It's going to be a half r squared going from zero to a d theta We can certainly bring this h out now also. We can bring the half out as well and We can this is going to be a squared minus zero squared Now the a is also a constant so that can also come out and all we left with is the zero to two pi d theta That's all we have left. That's going to be an h over two That is going to be an a squared and that's gonna be a theta going from zero to two pi in other words an H over two and a squared and a two pi Eventually, what are we left with? We are left with Pi a squared to h and remember this a represented the radius that is pi r squared h And that is the equation of the volume of a cylinder Changing from a Cartesian coordinate system to a polar coordinate system Just remembering the only difference we did is to calculate at the area of tiny little infinitesimally little tiny little rectangles in a different way