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

question 44

Multiple Choice

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve $C$ . $\oint _ { C } ( 6 x y + 5 \ln ( 1 + x ) ) d x + 2 x ^ { 2 } d y$ , where $C$ is the cardioid $r = 2 + 2 \cos \theta$ .

• A) \(- 20 \pi\)
• B) \(- 80 \pi\)
• C) \(- 10 \pi\)
• D) \(- 40 \pi\)

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