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Homework Help: Hard Surface Integral Problem

  1. Apr 17, 2013 #1
    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. jcsd
  3. Apr 17, 2013 #2


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    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 = ??##.
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