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Spherical Coordinates Triple Integral

  1. Aug 3, 2008 #1
    I thought this question was elementary... but I apparently know less than I thought I did.

    1. The problem statement, all variables and given/known data
    Use spherical coordinates to evaluate [tex]\iiint_{E} x^{2}+y^{2}+z^{2}dV[/tex]
    Where E is the ball [tex]x^{2}+y^{2}+z^{2}\leq 16 [/tex]


    2. Relevant equations
    [tex]x^{2}+y^{2}+z^{2}=\rho^{2}[/tex]



    3. The attempt at a solution
    [tex]\int^{2\pi}_{0}\int^{\pi}_{0}\int^{4}_{0}\left(\rho^{2}\right)\rho Sin \left( \phi \right) d\rho d\phi d\theta = 256\pi[/tex]

    which is apparently incorrect. Where am I going wrong?
     
  2. jcsd
  3. Aug 3, 2008 #2

    Hootenanny

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    You may want to check your volume element :wink:.
     
  4. Aug 3, 2008 #3
    Am I blind? I don't understand.
     
  5. Aug 3, 2008 #4
    [tex]\left(\rho^{3}\right) \rho[/tex] instead of [tex]\left(\rho^{2} \right) \rho [/tex] gets me the right answer... but why?
     
  6. Aug 3, 2008 #5
    Oh... :rolleyes:
     
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