According to Green's Theorem, the line integral $\int _ { C } y d x + x d y$ 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) $2 x + 2 y$

Question

According to Green's Theorem, the line integral $\int _ { C } y d x + x d y$ 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) $2 x + 2 y$

Quizplus · Accepted Answer

The Answer of According to Green's Theorem, the line integral $\int _ { C } y d x + x d y$ 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) $2 x + 2 y$

According to Green's Theorem, the Line Integral ∫Cydx+xdy\int _ { C } y d x + x d y∫C​ydx+xdy

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