00:01
Here's what we have, okay? we're using spherical coordinates here, so we know theta is all around.
00:12
There's the 2 pi, and then phi is this angle right here, and it comes from the, it comes from the z is equal to x squared plus y squared, and that's z is rho cosine phi, and square root of x squared plus y squared is rho sine phi, so tangent of phi is 1, so phi is 45, or pi over 4.
00:41
So phi is changing from 0 to pi over 4, and then rho, rho is changing from, okay, rho comes from the z, okay? z is equal to 1, so z is rho cosine phi, so that means rho is changing from 1 over cosine phi to 2 over cosine phi.
01:10
So that integral becomes 0 to 2 pi, 0 to pi over 4, and 1 over cosine phi to 2 over cosine phi, rho square sine phi, d rho, d phi, d theta...