Why is the last term on the RHS missing in my evaluated triple integral?

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    Integral Triple integral
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SUMMARY

The discussion centers on the evaluation of a triple integral related to a deformable control volume equation, specifically addressing an error in the application of Maple software. David, the user, incorrectly evaluated the integral, leading to a missing term on the right-hand side (RHS) of the equation. The correct approach involves recognizing that L is a function of time, L(t), and applying Leibniz's rule for differentiating integrals with variable limits. This clarification resolves the discrepancy in the evaluated results.

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David Fishber
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Hi,
I'm having a problem in evaluating a triple integral for a deformable control volume equation:
}{\mathrm{d}&space;t}\int_{0}^{H}\int_{\frac{-W}{2}}^{\frac{W}{2}}\int_{0}^{L}\rho&space;vdxdydz.gif


where v is defined as:
y}{W})^{2}&space;\right&space;]\frac{z}{H}\left&space;(&space;2-\frac{z}{H}&space;\right&space;).gif


When I evaluate the triple integral in Maple and by hand I get:
gif.gif


The correct answer is:
gif.gif


Can someone please explain where the last term on the RHS comes from??

Thanks in advance,
David
 
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If you make the integration, you end up with:
[tex]\frac{d}{dt}(\rho{WH}L\frac{dL}{dt})[/tex]
Thus, you have done this incorrectly (and given incorrect information to Maple).

This is where your flaw is to be found:
Remember that L=L(t), meaning you need to use Leibniz' rule for differentiating an integral with variable limits correctly.
 
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