Originally Posted by

**purplerain** Here is the promblem

$\displaystyle F(x,y,z) = xz i + yz j + 3z^2 k $

$\displaystyle E\ is\ the\ solid\ bounded\ by\ the\ paraboloid\ z\ = x^2 + y^2\ and\ the\ plane\ z = 1 $

$\displaystyle \int\int F \cdot dS = ? $

Divergence Theorem which i really don't understand well is $\displaystyle \int\int F \cdot dS = \int\int\int div\ F\ dV $

I went ahead and got the gradient vector which is $\displaystyle <z,z,6z> $ and then the function i got when i set up the triple integral is $\displaystyle 8\int\int\int z dV$

and i guess all that is left for me to do is to set up and integrate. Math experts am im right up until this part, and if i am help me set up the triple integral. I'm assuming i have to switch to polar coordinates, i hope i don't have to switch to spherical or cylindrical coordinates, because i really don't understand that stuff very well!