00:01
So we're going to be evaluating the surface integral.
00:03
What we have here are two integrals, and we know that this is going to be x, y, z, s.
00:16
We know that how this is going to look for the surface integral is it will be f of r, of u and v, times the cross product of r -u -r -v, d -a.
00:34
So based on all this, we first want to find x of u and v.
00:41
So create this parametric equation.
00:44
We know that that's u cosine v.
00:48
So based on that, we want to take the partial derivative of x with respect to you.
00:54
We get cosine v, and then we want to take the partial derivative of x with respect to v, and we get a negative u sine v.
01:00
We do the same process for the partial derivatives of y with respect to unv.
01:06
We get sine v and u cosine v respectively.
01:10
And then we want to do the same thing with z, you and v, so we'll end up getting 1 and 0 for the partial derivatives.
01:19
So based on that, we see that our u is going to be equal to, it's going to be a vector, it'll be cosine v, sine v, sine v, and then rv is going to be another vector, which will be a negative u, sine, v, u, cosine, v, and zero...