Compute the Integral Using Green's Theorem $\int _ { C } \vec { F } \cdot d \vec { r }$

Short Answer

Compute the integral using Green's theorem. $\int _ { C } \vec { F } \cdot d \vec { r }$ , where C is the square with vertices (1, 1), (0, 1), (0, 0), and (1, 0) traversed counterclockwise and $\vec { F } ( x , y ) = \left\langle x ^ { 2 } y , x ^ { 2 } y ^ { 2 } \right\rangle$