Use Stoke's Theorem to Evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$

Short Answer

Use Stoke's theorem to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ $\mathbf { F } ( x , y , z ) = 6 y x ^ { 2 } \mathbf { i } + 2 x ^ { 3 } \mathbf { j } + 6 x y \mathbf { k }$ C is the curve of intersection of the hyperbolic paraboloid $z = y ^ { 2 } - x ^ { 2 }$ and the cylinder $x ^ { 2 } + y ^ { 2 } = 25$ oriented counterclockwise as viewed from above.