00:01
So we have the following region.
00:06
We have here all this y.
00:12
Here the x or y, the c axis.
00:21
And we have a region that is, it has the upper bound to be this paraboloid that this paraboloid here is described by c.
00:41
C is equal to x squared plus y squared and then the lower bound is this plane c is equal to zero very nice we have that and then we also have that is inside of the cylinder over this one so that we have a cylinder here over this one that uh cuts this one so that we're going to obtain a region like a city shown there so this region it's called it d so you want to find what is the volume so you could do cylindrical coordinates where all we plot here c and r the distance to the c axis we notice that this can it has to be like this where this is the line r equals 1 is equal to this line and we have this region this is all this area and this this is a all that is r square so this would be the line c is equal to r square so that no we have that picture picture and then we rotate that around theta to obtain so well, the way we could do this is that we could say, well, c is going to be between 0 and r squared, and then all r goes from 0 up to 1.
02:51
R goes from 0 up to 1, and theta goes all the way around.
02:58
So all the way from 0 to 2 pi, theta would go between 0 and 2 pi.
03:11
So that this volume would be equal to cylindrical coordinates...