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

Short Answer

Use Stokes' Theorem to evaluate $\int _ { C } \mathbf { F } \cdot d \mathbf { r }$ where $\mathbf { F } ( x , y , z ) = x ^ { 2 } z \mathbf { i } + x y ^ { 2 } \mathbf { j } + x ^ { 2 } \mathbf { k }$ and C is the curve of intersection of the plane $x + y + z = 1$ and the cylinder $x ^ { 2 } + y ^ { 2 } = 9$ .