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

question 152

Short Answer

Use Stokes' Theorem to evaluate $\iint _ { S } \operatorname { cur } \mathbf { F } \cdot d \mathbf { S }$ .
$$\mathbf { F } ( x , y , z ) = 6 x y \mathbf { i } + 5 y z \mathbf { j } + 2 z ^ { 2 } \mathbf { k }$$
$S$ is the part of the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ lying below the plane $z = 6$ and oriented with normal pointing downward.