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 in the plane $z = 6 - x - y$ lying above the square with vertices (0, 0), (1, 0), (1, 1), and (0, 1) with the normal vector in the positive z direction where $\vec { F } ( x , y , z ) = \langle z , y , 2 x \rangle$