Using Green's Theorem, the Line Integral $\int$ C $x ^ { 2 } y d x - y ^ { 2 } x d y$

Multiple Choice

Using Green's Theorem, the line integral $\int$ C $x ^ { 2 } y d x - y ^ { 2 } x d y$ where C is the closed curve consisting of the arc of $4 y = x ^ { 3 }$ from (0, 0) to (2, 2) and the line segment from (2, 2) to (0, 0) , is

A) $- \frac { 32 } { 15 }$
B) $- \frac { 28 } { 15 }$
C) $- \frac { 26 } { 15 }$
D) $- \frac { 24 } { 15 }$
E) $- \frac { 22 } { 15 }$