00:01
Alright, so to find our volume, we're going to use the equation of pi from x1 to x2 of y squared dy or dx.
00:14
So it's going to be pi from 0 to pi over 4 of the square root of x cosine 2x and square that.
00:33
So now we're going to have just x cosine 2x dx.
00:40
So let's use integration by parts.
00:43
So we're going to have u and dv.
00:52
So let's let our x be u and our dv be cosine of 2x.
00:58
So when we find du, that's just dx.
01:03
And then when we integrate cosine 2x, we'll use a u sub here.
01:08
So that u be 2x, du is 2 dx.
01:17
So du over 2 is equal to dx.
01:19
So now we're going to have cosine of u times du over 2.
01:28
When we integrate that, we end up with 1 half sine of u, which is just 1 half sine of 2x...