Let $\mathbf { F } ( x , y , z ) = - y \mathbf { j } + x \mathbf { j } + e ^ { z ^ { 2 } } \mathbf { k }$

question 109

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = - y \mathbf { j } + x \mathbf { j } + e ^ { z ^ { 2 } } \mathbf { k }$ . Evaluate $\iint _ { S } \operatorname { curl } \mathbf { F } \cdot \mathrm { d } \mathbf { S }$ over the surface S given by $z = \sqrt { 1 - x ^ { 2 } - y ^ { 2 } }$ , with downward orientation.

• A) \(2 \pi\)
• B)\(\pi\)
• C)\(\frac { \pi } { 2 }\)
• D)\(3 \pi\)
• E) \(- 2 \pi\)
• F) \(- \pi\)
• G)\(- \frac { \pi } { 2 }\)
• H)\(- 3 \pi\)

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