Green's Theorem to Evaluate the Integral $\int _ { C } \left( x ^ { 2 } - y ^ { 2 } \right) d x + 10 x y d y$

question 52

Multiple Choice

Green's Theorem to evaluate the integral $\int _ { C } \left( x ^ { 2 } - y ^ { 2 } \right) d x + 10 x y d y$
for the path $C : x ^ { 2 } + y ^ { 2 } = 64$ .

• A) \(512 \pi\)
• B) 0
• C) 8
• D) \(64 \pi\)
• E) 512

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