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

question 168

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) \(- 6 \pi\)

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