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

question 224

Multiple Choice

According to Green's Theorem, the line integral $\int _ { C } x ^ { 2 } d x + y ^ { 2 } d y$ 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)\(1\)
• F)\(2 x + y\)
• G)\(x + 2 y\)
• H) \(2 x + 2 y\)

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