- #1

Damascus Road

- 120

- 0

evaluating [tex]\int\int\int \nabla . V d\tau[/tex] over

[tex]x^{2} + y^{2} \leq 6, 0 \leq z \leq 10 [/tex]

where V is a vector function of just [tex]\hat{x} [/tex] and [tex] \hat{y}[/tex].

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!