00:01
All right, so first of all, we're given a parabola.
00:06
We're given our function x squared.
00:09
Y equals x squared.
00:10
We're bound by y equals zero and x equals two.
00:14
So we have our x squared function, but we're bound by x equals two and y equals zero.
00:34
So we know this distance here is two.
00:36
And when we rotate about the x -axis, that helps us know our radius.
00:43
But we also know that up here we should be at y equals four.
00:48
So our vertical radius here, when we take our cross -sections, is going to be four, our maximum vertical radius.
00:59
All right, but our radius is given to us by the function x squared.
01:03
So y equals x squared.
01:08
Now setting this initial problem up, it's pretty straightforward.
01:14
We're bound from 0 to 4, and it is going to be pi times x squared dx.
01:26
That's a pretty straightforward integral.
01:28
Move our pi out front from 0 to 4 of x squared dx.
01:36
We get pi times x cubed over 3 from 0 to 4.
01:44
You can type this into a calculator.
01:49
So we get 4 cubed divided by 3.
01:57
And that is approximately 64 over 3.
02:00
So our solution, part a, is 64 pi over 3...