Evaluating triple integral

[David Fishber]

Hi,
I'm having a problem in evaluating a triple integral for a deformable control volume equation:

where v is defined as:

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

The correct answer is:

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

Thanks in advance,
David

 

[arildno]

If you make the integration, you end up with:
$$\frac{d}{dt}(\rho{WH}L\frac{dL}{dt})$$
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.