Why this triple integral equals zero?

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Discussion Overview

The discussion revolves around a triple integral that yields different results when computed numerically and when transformed into spherical coordinates. Participants explore the reasons behind the discrepancy in results, focusing on the transformation process and the properties of the functions involved.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant reports that numerical integration yields zero, while spherical coordinates give a result of pi^2 / 40, expressing confusion over this difference.
  • Another participant requests clarification on the transformation process and the limits used in spherical coordinates, suggesting that the differential volume element may not have been transformed correctly.
  • A third participant asserts that the first two integrations are straightforward and lead to an odd function of x, implying that this could explain why the integral evaluates to zero.
  • The original poster acknowledges the feedback and indicates they found an explanation after rechecking their calculations in spherical coordinates.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the reasons for the differing results, as the discussion includes multiple viewpoints regarding the transformation and properties of the integral.

Contextual Notes

There are unresolved questions regarding the proper transformation of the integral and the handling of the differential volume element in spherical coordinates.

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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.
 
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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:
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.
 
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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