Use Stoke's Theorem to Evaluate $\iint _ { S } \mathbf { F } \cdot d r$

Short Answer

Use Stoke's theorem to evaluate $\iint _ { S } \mathbf { F } \cdot d r$ .
$\mathbf { F } ( x , y , z ) = 4 z \mathbf { i } + 2 \mathbf { j } + 6 y \mathbf { k }$
$C$ is the curve of intersection of the plane $z = x + 9$ and the cylinder $x ^ { 2 } + y ^ { 2 } = 9$