Use the Divergence Theorem to Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

Multiple Choice

Use the Divergence Theorem to evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ where $\mathbf { F } ( x , y , z ) = x ( y - 1 ) \mathbf { i } + 2 y z \mathbf { j } - \left( z ^ { 2 } + y z \right) \mathbf { k }$ and S is the surface of the cylinder $x ^ { 2 } + y ^ { 2 } = 4$ , bounded by the planes $z = 0$ and $z = 3$ .

A) $12 \pi$

B) $4 \pi$
C) $- 3 \pi$
D) $6 \pi$
E) $- 12 \pi$
F) $- 4 \pi$

G) $3 \pi$

H) $- 6 \pi$