# Flux through surface

## Homework Statement

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

## The Attempt at a Solution

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