Use Green's Theorem to Evaluate the Line Integral Along the Positively

Multiple Choice

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. $\oint _ { C } e ^ { x ^ { 2 } } d x + \left( \sin y - 4 x ^ { 2 } \right) d y$ , where C is the boundary of the region bounded by the parabolas $y = x ^ { 2 }$ and $x = y ^ { 2 }$ .

A) $- \frac { 12 } { 5 }$ + e
B) $- \frac { 6 } { 5 }$ + e
C) $- \frac { 6 } { 5 }$
D) $- \frac { 12 } { 5 }$