Originally Posted by

**arbolis** Verify the divergence theorem for $\displaystyle F(x,y,z)=(xz,yz,3z^2)$ in the solid $\displaystyle E$ limited by the paraboloid $\displaystyle z=x^2+y^2$ and the plane $\displaystyle z=1$.

My attempt : They ask me the check that $\displaystyle \int_{\partial E} F \bold n dE= \iiint _E div F dE$ holds.

I've already calculated the right hand side, which gave me $\displaystyle \frac{8\pi}{3}$.

I'm stuck on the left side. I know that $\displaystyle \int_{\partial E} F \bold n dE$ is a double integral. I think that I must parametrize the surface $\displaystyle E$ and calculate $\displaystyle \bold n$. How do I find $\displaystyle \bold n$ ? By calculating the gradient of $\displaystyle F$? I'm not sure at all about this approach though. Can you confirm it?