Flux through surface

1. The problem statement, all variables and given/known data

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

2. Relevant equations



3. The attempt at a solution

[tex] \int\limit_R ((x^2+x^2)\vec{i} + 7\vec{j} - zx\vec{k}) \cdot (-2x\vec{i} -2z\vec{k} + \vec{j})dA [/tex]

 

thanks!