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Surface Integral (Integral Setup)

  1. Oct 21, 2016 #1
    1. The problem statement, all variables and given/known data
    I'm just required to setup the integral for the question posted below

    2. Relevant equations

    3. The attempt at a solution
    So solving for phi @ the intersection of the sphere and the plane z=2:

    z = pcos(phi)
    2 = 3cos(phi)
    phi = arccos(2/3)

    so my limits for phi would go from 0 to arccos(2/3)

    and my limits for theta would go from 0 to 2pi

    for the surface integral dS would become 9sin(phi)

    The rest of the integral I can obtain from just substituting x = psin(phi)cos(theta) y = psin(phi)sin(theta) and z = pcos(phi)

    What I really want to be sure of is limits of integration.

    Thanks in advance guys

    Attached Files:

  2. jcsd
  3. Oct 21, 2016 #2


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    I hope you mean ##9 \sin\phi \;
    d\theta d\phi## :rolleyes:
    The latter for the numerator. The denominator is simply 9 -- easy !
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