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

question 79

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) \(91 \pi\)

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