# Homework Help: Surface Integral

1. May 9, 2013

### flaxstrax

1. The problem statement, all variables and given/known data
Find integral I = ∫∫xz^2 dydz + (x^2y − z^3) dzdx + (2xy + y^2z) dxdy (Integrate over A)
if A is half a sphere(radius is a). Sphere is given with equation z=(a-x^2-y^2)^1/2 and z=0.

2. Relevant equations
The excercise is in 2 parts , find it with just integrating and b) applying gauss's law.

3. The attempt at a solution
I just cant understand how i get it ... Every way i can think of , gives me wrong answer, I have to find scalar. If i substitute x from the sphere equation , then in integration bounds it still remains ?
I know this aint much to go on but help me. Just tell me what i can substitute so i can find this ingtegral or is it even possible ? I dont need whole excercise, i can integrate myself.

2. May 10, 2013

### HallsofIvy

I would do this as three separate integrals: Doing the "dydz" integral y will go from -a to a and, for each y, z will go from 0 to $\sqrt{a^2- y^2}$. And, of course, for each y and z, $x= \sqrt{a^2- y^2- z^2}$. The first integral is
$$\int\int xz^2 dydz= \int_{y=-a}^a\int_{z= 0}^\sqrt{a^2- y^2} z^2\sqrt{a^2- y^2- z^2}dzdy$$
and similarly for the other two integrals.

3. May 10, 2013

### flaxstrax

4. May 11, 2013

### flaxstrax

Did it with spherical coordinates now . Tthis is so impossible :(