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

Short Answer

Use Stokes' Theorem to evaluate $\iint _ { S } \operatorname { cur } \mathbf { F } \cdot d \mathbf { S }$ . $\mathbf { F } ( x , y , z ) = 4 x y \mathbf { i } + 5 y z \mathbf { j } + 2 z ^ { 2 } \mathbf { k }$ ;
S is the part of the ellipsoid $9 x ^ { 2 } + 9 y ^ { 2 } + 4 z ^ { 2 } = 36$ lying above the xy-plane and oriented with normal pointing upward.