Use the Divergence Theorem to Calculate the Surface Integral $\iint _ { s } \mathbf { F } \cdot d \mathbf { S }$

Short Answer

Use the Divergence Theorem to calculate the surface integral $\iint _ { s } \mathbf { F } \cdot d \mathbf { S }$ ; that is, calculate the flux of $\mathbf { F }$ across $S$ .
$$\mathbf { F } ( x , y , z ) = x y e ^ { z } \mathbf { i } + x y ^ { 2 } z ^ { 3 } \mathbf { j } - y e ^ { z } \mathbf { k }$$
$S$ is the surface of the box bounded by the coordinate planes and the planes $x = 6 , y = 2$ and $z = 1$ .