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Triple integral trouble

  1. Nov 9, 2004 #1
    [tex]\iiint {\sqrt(R^2 - 2aR\cos\theta + a^2)} R^2 \sin\theta\,dR\,d\theta\,d\phi[/tex]

    with the integration over R between 0 and a
    the integration over between 0 and pi
    the integration over between 0 and 2pi

    Should I use integration by parts or should I take the R^2 sin(theta) under the square root?

    Any hints and tips are much appreciated!
     
  2. jcsd
  3. Nov 9, 2004 #2

    arildno

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    Do the [tex]\theta[/tex] integration first (note that the sine outside the root makes this easy).

    Beware absolute values in your R integration!
     
  4. Nov 9, 2004 #3
    Do I need to change the order of integration then and have new limits or can I choose to rearrange it to a more convenient form, like

    [tex]\iiint {\sqrt(R^2 - 2aR\cos\theta + a^2)} R^2 sin\theta\,d\theta\,dR,d\phi[/tex]

    then integrating wrt [tex]\theta[/tex] by parts?
     
  5. Nov 9, 2004 #4

    arildno

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    You don't do it by parts!!

    Note that your integrand equals:
    [tex]\frac{\partial}{\partial\theta}\frac{R}{3a}(R^{2}-2aR\cos\theta+a^{2})^{\frac{3}{2}}[/tex]
     
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