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I Why this triple integral equals zero?

  1. Sep 5, 2016 #1
    Hello everyone, I have the this inquiry:

    if I compute de following integral:
    http://micurso.orgfree.com/Picture1.jpg
    by numerical methods I get cero as a result. I used Maxima and Mathematica and their functions for numerical integration give me an answer equal to cero.
    But, if I apply transformation with spherical coordinates the result turns out to be equal to pi^2 / 40.
    I can't seem to find an explanation for this. Could any of you guys give me a hand with this? Thank you in advance.
     
  2. jcsd
  3. Sep 5, 2016 #2

    jedishrfu

    Staff: Mentor

    Well we'd need to see how you transformed the integral and its limits into spherical coordinates before we could even attempt to say what happened.

    One question I had was whether you transformed the dxdydz properly or not.

    https://en.m.wikipedia.org/wiki/Volume_element

    Where you can see that dXdydz transforms into:

    ##dV = \rho^2 sin \theta d\rho d\theta d\phi##
     
    Last edited: Sep 5, 2016
  4. Sep 6, 2016 #3

    DrClaude

    User Avatar

    Staff: Mentor

    The thread title asks why this is zero, which is quite easy to show. The first two integrations, over z and y, are trivial to do, and the result is an odd function of x.
     
  5. Sep 6, 2016 #4
    Thank you so much for your answers, I rechecked what I did this morning and I found out what happens when calculating the integral in spherical coordinates.

    Again, thank you so much for your time and cooperation, you guys rock!!!
     
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