00:01
We have y equals x to the minus k, which in the first quadrant looks like this.
00:05
Y equals zero and to the right of x equals 1.
00:09
So this area here.
00:11
And this time we're going to send it around the y axis.
00:15
So we're going to want to cut this way so that we can get shells, volume of the shell, 2 pi r, hd.
00:30
He is the thickness of the shell, which is the thickness of the slice, which is dx.
00:38
R is from the axis of rotation out to the slice, which is some x value.
00:44
H is the height, which is y, so x to the minus k.
00:52
And this time we're going to pile them up from 1 to infinity.
00:58
So volume is 2 pi, 1 to infinity, rht, so 2 pi limit as r -h -t.
01:12
1 to r, x to the minus k plus 1, dx, 2 pi, pi, limit is r goes to infinity, x to the minus k plus 2 over minus k plus 2, from 1 to r...