Compute the flux of the vector field, $\displaystyle \vec{F} $, through the surface, S. $\displaystyle \vec{F} = y\vec{i} + 7\vec{j} - xz\vec{k}$ and S is the surface $\displaystyle y = x^2 + z^2$ with $\displaystyle x^2 + z^2 \leq 36$ oriented in the positive y direction.

My answer:

$\displaystyle \int\limits_R ((x^2+z^2)\vec{i} + 7\vec{j} - xz\vec{k}) \cdot (-2x\vec{i} - 2z\vec{k} + \vec{j}) dA $

I don't know if this is correct...