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

question 64

Short Answer

Use Stokes' Theorem to evaluate $\iint _ { S } \operatorname { curl } \mathbf { F } \cdot d \mathbf { S }$ S consists of the top and the four sides (but not the bottom) of the cube with vertices $( \pm 9 , \pm 9 , \pm 9 )$ oriented outward. $\mathbf { F } ( x , y , z ) = 4 x y z \mathbf { i } + 4 x y \mathbf { j } + 4 x ^ { 2 } y z \mathbf { k }$

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