# Volume integral, am I doing this right?

1. Sep 27, 2010

Hi all,

evaluating $$\int\int\int \nabla . V d\tau$$ over

$$x^{2} + y^{2} \leq 6, 0 \leq z \leq 10$$

where V is a vector function of just $$\hat{x}$$ and $$\hat{y}$$.

Using the divergence theorem, and doing the dot product of V with the normal of the first surface,

the two partials w.r.t x and y are 2x and 2y,
doing the cross product, the normal is 4xy z.

So, the dot product is zero since there is no z component to V?

Then, when I go to do the same for the second surface, I'm not sure what my double integral limits are, since I only have a surface of z.....

help!
thanks!