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

Multiple Choice

Compute the integral using Green's theorem. $$\int _ { C } \vec { F } \cdot d \vec { r }$$ , where C is the triangle with vertices (1, 1) , (0, 0) , and (1, 0) traversed counterclockwise and $\vec { F } ( x , y ) = \left\langle x ^ { 2 } y , x ^ { 3 } y ^ { 3 } \right\rangle$

A) $- \frac { 1 } { 7 }$
B) $\frac { 1 } { 7 }$
C) $- \frac { 1 } { 14 }$
D) $\frac { 1 } { 14 }$