Use Stoke's Theorem to Evaluate $\iint _ { S } \mathbf { F } \cdot d r .$

Short Answer

Use Stoke's theorem to evaluate $\iint _ { S } \mathbf { F } \cdot d r .$ $\mathbf { F } ( x , y , z ) = 2.56 x \mathbf { i } + 16 y \mathbf { j } + 4 \left( y ^ { 2 } + x ^ { 2 } \right) \mathbf { k }$ C is the boundary of the part of the paraboloid $z = 2.56 - x ^ { 2 } - y ^ { 2 }$ in the first octant. C is oriented counterclockwise as viewed from above.