Given that F(x, y)=-y-xy and C is the circular are joining the points (1,0) to (0,1)...

 

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Given that F(x, y)=-y-xy and C is the circular are joining the points (1,0) to (0,1) in counter clockwise direction. a) Evaluate the line integral of the vector field F(x, y) along the given path C by direct integration. b) Solve a) by using the Green's Theorem. Given that F(x, y)=-y-xy and C is the circular are joining the points (1,0) to (0,1) in counter clockwise direction. a) Evaluate the line integral of the vector field F(x, y) along the given path C by direct integration. b) Solve a) by using the Green's Theorem.