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

Essay

Use Stokes' theorem to evaluate $\int _ { C } \vec { F } \cdot d \vec { r }$ , where C is the boundary curve of the surface $S = \{ ( u v , u , u - v ) : 0 \leq u \leq 1 \text { and } 0 \leq v \leq 1 \}$ with the normal vector in the positive z direction where $\vec { F } ( x , y , z ) = \langle x , x , y \rangle$