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

Multiple Choice

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 $\vec { F } ( x , y , z ) = \left\langle z , y ^ { 2 } , 3 x \right\rangle$

A) 1
B) $- 1$
C) $- 2$
D) 2