Triple Integral Evaluation: Where Did I Go Wrong?

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Homework Help Overview

The discussion revolves around the evaluation of a triple integral, with participants examining the correctness of calculations and integration steps. The subject area pertains to multivariable calculus and integration techniques.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are reviewing the original poster's calculations and questioning specific multiplication and integration steps. There is a focus on identifying potential errors in the transition between different forms of the integral result.

Discussion Status

Some participants have pointed out discrepancies in the calculations, suggesting that the original poster may have made an error in multiplying constants. There is an acknowledgment of a possible correction to the final result, but no consensus has been reached on the correct answer yet.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can share or the methods they can use to verify their results.

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Homework Statement



http://img19.imageshack.us/img19/2559/triple.th.jpg

Homework Equations





The Attempt at a Solution



I get 16pi/3 (sqrt(2) -1) as the final result, but when I input the answer to the computer, it doesn't accept it. Am I doing a wrong integration/calculation anywhere? I double checked and I can't to find anything wrong.
 
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It seems that when you multiplied by 2pi, you said 16/3* 2pi=16pi/3...that's not really true is it?:wink:
 
oh so it should be 32pi/3 then.. thanks for pointing out the silly mistake
 
You went from
-\frac{1}{3}\left(4^{3}{2}-8^{3}{2})-\frac{8}{3}
to
\frac{16}{3}(\sqrt{2}-1)
instead of
\frac{8}{3}(2\sqrt{2}-1)
 

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