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

question 57

Multiple Choice

Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C. $\oint _ { C } ( 6 x y + 8 \ln ( 1 + x ) ) d x + 4 x ^ { 2 } d y$ , where C is the cardioid $r = 3 + 3 \cos \theta$ .

• A) 270 \(\pi\)
• B) \(135\) \(\pi\)
• C) \(\frac { 135 } { 4 }\) \(\pi\)
• D) \(\frac { 135 } { 2 }\) \(\pi\)

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