Use Stokes' Theorem to Evaluate $\iint _ { S } \operatorname { curl } \mathbf { F } \cdot d \mathbf { S }$

Use Stokes' Theorem to evaluate $\iint _ { S } \operatorname { curl } \mathbf { F } \cdot d \mathbf { S }$ $\mathbf { F } ( x , y , z ) = 7 x y \mathbf { i } + 7 e ^ { x } \mathbf { j } + 7 x y ^ { 2 } \mathbf { k }$ S consists of the four sides of the pyramid with vertices (0, 0, 0) , (3, 0, 0) , (0, 0, 3) , (3, 0,3) and (0, 3, 0) that lie to the right of the xz-plane, oriented in the direction of the positive y-axis.

A) 0
B) 12
C) 16
D) 49
E) 1

Correct Answer:

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