Use Green's Theorem And/or a Computer Algebra System to Evaluate $\int _ { C } x ^ { 2 } y d x - x y ^ { 2 } d y$

question 37

Multiple Choice

Use Green's Theorem and/or a computer algebra system to evaluate $\int _ { C } x ^ { 2 } y d x - x y ^ { 2 } d y$ , where $C$ is the circle $x ^ { 2 } + y ^ { 2 } = 64$ with counterclockwise orientation.

• A) \(8 \pi\)
• B) \(64 \pi\)
• C) \(2 \pi\)
• D) \(- 32 \pi\)
• E) None of these

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