00:01
And this problem, we're going to be evaluating the integral, the surface integral, and more particular.
00:10
We can see how far back we can go to get to the formula.
00:13
Since we can't get the formula, we'll rewrite it.
00:16
So it's going to be the double integral of f of x, y, g of x, y, so another function of x and y.
00:28
And then that's going to be times the square root of the part of the part of the number.
00:34
Derivative of z or the partial derivative of g with respect to x squared plus the same thing the only difference is it'll be the partial derivative with respect to y that's going to be plus 1 d a so we'll copy and paste this because this will be the formula that we're going off of we see that since we have our hemisphere we're given initially that our f of x y z is going to be x squared z plus y squared z so we'll have if we factor that out though we'll have x squared using distributive property we'll have x squared plus y squared times z and we know z based on the formula we're given if we solve for it will be the squared root of 4 minus x squared minus y squared.
01:56
And then we also want to take dgdx or dzdx, and this is the partial derivatives.
02:03
So what we end up getting once we simplify all of this, just through squaring and then combining like terms and simplifying, we will get 4 over 4 minus x squared minus y squared.
02:22
B -a.
02:25
And then this, since we know that 4, the square root of 4 minus x squared minus y squared is just z squared or the fact that these can cancel out right here, what will be left with is canceling these...