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Surface integrals in spherical coordinates

  1. May 2, 2006 #1

    I am studying for finals and I'm having trouble calculating flux over sections of spheres. I can do it using the divergence theorem, but I need to know how to do it without divergence thm also.

    The problem is, when calculating a vector field such as F(x, y, z) = <z, y, x>, say over the unit sphere (x^2 + y^2 + z^2 = 1), I always end up with weird terms like sin^3(phi) and cos^2(phi)sin(theta) that must be integrated

    So, is this normal? Should I memorize integrals for sin^3(phi) and such, or is there an easier method?

  2. jcsd
  3. May 2, 2006 #2


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    Integrating sin^3(phi) is not difficult. You know sin^3(phi) = sin^2(phi)*sin(phi) = (1-cos^2(phi))sin(phi). Then just use u-substitution with u = 1-cos^2(phi)
  4. May 2, 2006 #3
    *sigh* I guess it is easy. For some reason it just seems...unnecessary...
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