So, Alva, this cylinder between Well, I mean cylinder Nina. Three dimensional space in our free is described by the equation X squared plus C squared. Is he called the 10 on. Do you want to find the area with the portion portion off the cylinder? That between, uh, why equals to minus one on why equals one? Also, let's sketch how this could look like. So we have here the x axis. See taxes going up? Yes. See, on the y axis going along there, That direction So it increases in that direction. Increase in that direction increases in that. So this, uh, in the XY plane that can be seen as a let's take. Why the plane? Why he called zero corresponds to the explain excessive plane. So order is a circle of radius. Um, Tennessee Goto square root off 10 squared. So it is a circle of radius scores of 10. So you have this very nice circle in the the C X plane. Um, some circle of reduce square it off. 10. That is the length this length order on the all the conditions is that it is this this circle of the cylinder between the goes minus one on one s. So we're gonna have, uh, something standard, probably along y e. So we're gonna have a portion off the ceiling. They're like, uh, BCE, you know? So, uh, well, should look something like this Say something that are goes around there. She want to find the the area of this, uh, off the cylinder. Uh, area. So for that, we can do a final decision. Since citizen two dimensional object in r three, we convert, try, sit in terms off there's off some bible you on some angle. So two pouches So you could say Well, for the angle, we're going to say that exist ical to square it off game that is the radius. Then times cause sign of that angle on. Then why No see, she will be ableto spirit off. 10. Um, sign of that angle sign of, you know, on the novel. Why, it just goes, Why? Why? Why would go to you? Okay. To have these survivals, the angle Thera and you and so well, the the area is gonna be people toe integrate all the bounds for for Sarah are gonna be that, uh, Australia has to go all the way around to make full circle. So the angle Ferre is measured eyes measuring uh, the distance to the X axis. So it will be We have a portion That of things like these. The angle said I would be the single so fed out need to go single from zero up to two pi to have the whole term the whole circle on the unknown, or being go between uh minus one on one minus 11 So should be should be like Holland. So here to buy the area that village the Sierra and then for B B T minus 11 TV on the immunity integrator here the a spark of our little with our view This'll piece here corresponds to the differential of area on dso All this quantity is gonna be well that can be computed as the following determinant. We right, I dedicate e. I mean, how long this role we're gonna right? Alpha that are the relatives of the components with respect to theta I'm along this sec The third role are severely active. All the components with respect to use all the devolved um effects with respectable there would be squared off 10 My sign It's gonna be minus squared off 10 Shine Vera Yeah. Uh, off. So why or zero under a devolved see would be squared off thing cause And then for the for you off this is should be not be better You this by always. You you Yeah, um this this would be York. Yeah, so I mean, I'm just saying it's not It's not really that you So, uh, there to cover the components in respect to you. So they develop X with respect to use you. They had to know why, with respect to you would be one good the Z with respect to you with you So that this vector is gonna be the vector of all these times That so that minus times that zero for Jamie would have Ah, I am No or I It's items. So systems that minus that comes that's a minus spirit of pain, cause now, for J, it would be J that times that minus that times, that's o j zero on the NK. And so these times that minus at times that so minus Okay, I m c squared off 10. Um, I'm sign. Yeah, so that these things vector has alarmed a normal. This victory is gonna be squared off the components squared. Alright, together. So it's critical. Dam Square is gonna be 10 um, scores squared plus and I'm sine squared, which this can be simplified to 10 times. Course the square plus sine square. Very nice. This is people toe one course square person scores one. So these norm the norm is gonna be squared off. 10 Indiana. All the these would be photo. That area area is gonna be equal toe squared off. 10. Um, right. Do you deserve you the sierra? And then you goes from minus one upto one on terra goes from so you occupy. Well, this is ableto so we can pull out the spirit off. 10 internal off. Use you always getting minus one or one. Plans for the development. Just Sarah. Evaluating between to buy on zero so that these will be equal to squared off then thanks. One minus minus one minus minus one times. Um, by minus zero times to fight my minus serious to pilot. So this is equal toe one is minus minus. That becomes plus or you'll be, um, plus once it's gonna be to screw it off 10 times toe by. So it is equal to four squared off 10. And so bye. So that is gonna be theirry a off this question off cylinder. Uh, area. It's four kind of 10. Sorry.