According to Green's Theorem, the Line Integral $\int _ { C } y ^ { 2 } d x + x ^ { 2 } d y$

question 103

Multiple Choice

According to Green's Theorem, the line integral $\int _ { C } y ^ { 2 } d x + x ^ { 2 } d y$ over a positively oriented, piecewise-smooth, simple closed curve C is equal to the double integral $\iint _ { D } f ( x , y ) d A$ over the region D bounded by C. Find the function $f ( x , y )$ .

• A) \(2 x - y\)
• B) \(x - 2 y\)
• C) \(2 x - 2 y\)
• D) \(0\)
• E)\(2 x + y\)
• F) \(1\)
• G) \(x + 2 y\)
• H)\(2 x + 2 y\)

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