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Am I setting this integral up correctly?

  1. Oct 20, 2015 #1
    1. The problem statement, all variables and given/known data
    Use spherical coordinates to evaluate the integral over a sphere of radius R.

    2. Relevant equations
    The equation of my sphere would be x^2+y^2+z^2=R^2
    Please see the attached file.

    3. The attempt at a solution
    I have attached a file to show my work so far. Evaluating the integral once it is set up should be fine, I'm concerned it's not set up correctly. Thank you.
     

    Attached Files:

  2. jcsd
  3. Oct 20, 2015 #2

    BvU

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    Hello,
    You want to reconsider dV. ## \ \ \ dV \ne dr\, d\phi \,d\theta ##.
     
  4. Oct 20, 2015 #3
    I'm beginning to think that it's also not as easy as (pcos∂)^2 since my radius is R then p=R so isn't it ∫∫∫pcos∂)^2p^2
     
  5. Oct 20, 2015 #4
    Nope. You're integrating p over a radius of R. It's not the same thing.
     
  6. Oct 20, 2015 #5

    BvU

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    You are calculating a volume integral, so your p is running from 0 to R .

    Your function to integrate is ##\ f(r, \theta, \phi) = (r\cos\theta)^2## as you wrote correctly.

    Now check out how you can express a volume element in spherical coordinates ##dV(r, \theta, \phi)## , e.g. as shown here or here
     
  7. Oct 20, 2015 #6
    So it would then be (rcosθ)^2r^2sinθdrdθdphi which becomes r^2sinθcosθdrdθdphi and then become r^2sin(2θ)/2drdθdphi
     
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