00:01
The way to approach this problem is that we have the square root of y.
00:05
So the way i'm reading it is 8 square root y is like this.
00:09
And they want you to revolve this about the x -axis using shells.
00:13
So what the shell is going to look like is something like this.
00:18
And you're doing lateral area of a cylinder is what that is.
00:22
And so the formula is 2 .r .h.
00:25
And they even tell you to do it between 0 and 8, which is kind of nice.
00:32
So what we have is the volume will be the integral.
00:36
Well, i like to move that 2 pi in front first, from 0 to 8.
00:40
Of the radius of each one of these cylinders is y.
00:44
And then the height of each one of these cylinders is that function 8 root y, d .y.
00:50
So before i actually find the integral and find the volume, what i would do is think of this instead of the square root as to the one -half power.
00:59
So when you multiply at the same base, you can add those x...