00:01
Okay, i think cylindrical coordinates is the best because let's look at the xy region here.
00:09
Xy is x is changing from 0 to a and y is changing the semicircle.
00:20
So this is the region, okay? that means in the xy plane, so theta is going to be 0 to pi over 2, quarter circle.
00:37
R is going to be 0 to a and z is already given, a squared minus.
00:46
So 0 to a squared minus x squared plus y squared is r squared, so r squared.
00:55
So the integral is going to be like this, a squared minus r squared.
01:07
X squared is r squared cosine squared theta.
01:13
Then r dz dr d theta.
01:18
So start with this which is r cubed r to the fourth.
01:22
Well, i'm sorry, r cubed cosine squared theta times z which is a squared r squared.
01:33
Okay, now we're going to do dr which is a squared r to the fourth over 4 cosine squared theta minus r to the fifth.
01:51
So r to the sixth over 6 cosine squared theta from 0 to a which is going to give us r to the a to the sixth over 4 minus a to the sixth over 6.
02:10
I'm just going to take the cosine squared out...