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Triple integration over portion of Sphere

  1. Oct 4, 2016 #1
    1. The problem statement, all variables and given/known data
    upload_2016-10-3_19-5-13.png

    2. Relevant equations
    spherical Jacobean

    3. The attempt at a solution
    I have (sorry, have to capture my work, too hard to type)
    upload_2016-10-3_19-6-20.png

    then the integration of p3 ep2 = 1/2 ep2 (p2-3/2) ??
     
  2. jcsd
  3. Oct 4, 2016 #2
    The answer I got using cylindrical was eπ/8,
    but here, using the spherical, I got π(e+3)/64
     
  4. Oct 4, 2016 #3

    Ray Vickson

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    No. You can check that for yourself, by showing that the derivative is not ##r^3 \exp(r^2)##.

    Do integration by parts.

    BTW: I get ##\pi/8## using spherical coordinates.
     
  5. Oct 4, 2016 #4
    π/8 not πe/8 ?
     
  6. Oct 4, 2016 #5

    Ray Vickson

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    I wrote exactly what I meant.

    If you had a different upper bound of ##r = a## instead of ##r = 1## you would, indeed, get an exponential in the answer.
     
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