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

Essay

Compute the integral using Green's theorem. $$\int _ { C } \vec { F } \cdot d \vec { r }$$ , where C is the unit circle traversed counterclockwise and $\vec { F } ( x , y ) = \left\langle y ^ { 3 } , - x ^ { 3 } \right\rangle$