00:03
So for this problem, we're going to be evaluating a surface integral, and to do so, we're going to use the following formula.
00:21
So it'll be the double integral of f of g of y, z, y of z, times the square root of the partial derivative of x, or the partial derivative of g, with respect to y, z, squared, plus the, the partial derivative of g or the partial derivative of x with respect squared plus 1.
01:02
And with that, given what we have, we know that this is going to be 5 minus y times z.
01:25
And then evaluating this because we know that x equals 5 minus y, this is just going to be 0, and this is going to just be 1 .1.
01:36
So we'll end up getting.
01:37
The square root of 2, which we can bring out in front.
01:47
Then we want to change this to polar coordinates because we know that the region is inside.
01:54
We know that d, the region is a disk.
01:57
So we know the radius is between 0 and 3.
02:01
And since it's a disk, we'll have from 0 to pi, 0 to 3...