# Hard Surface Integral Problem

1. Apr 17, 2013

### jacksonb62

1. The problem statement, all variables and given/known data

Find the average value of the function f(x,y,z)=xyz on the unit sphere in the first octant

2. Relevant equations

I know that I need the surface integral of xyz over the sphere and then need to divide by the surface area of the region, but I'm having a hard time setting up the integration. We have always done surface integrals with double integrals, but for this I feel like spherical coordinates need to be used which I only know how to set up in a triple integral. Help please!

3. The attempt at a solution

2. Apr 17, 2013

### LCKurtz

Spherical coordinates with $\rho$ constant will only have two variables, giving a double integral. What is the formula for the element of surface area in spherical coordinates? $dS = ??$.