Use Green's Theorem to Evaluate the Line Integral $\int _ { C } \left( e ^ { - x ^ { 2 } / 2 } - y \right) d x + \left( e ^ { - y ^ { 2 } / 2 } + x \right) d y$

Multiple Choice

Use Green's Theorem to evaluate the line integral $\int _ { C } \left( e ^ { - x ^ { 2 } / 2 } - y \right) d x + \left( e ^ { - y ^ { 2 } / 2 } + x \right) d y$ where $C$ is the boundary of the region lying between the graphs of the circle $x = 8 \cos \theta , y = 8 \sin \theta$ and the ellipse $x = 6 \cos \theta , y = 4 \sin \theta$ .

A) $120 \pi$
B) $162 \pi$
C) $172 \pi$
D) $80 \pi$
E) $91 \pi$