Use the method of this example to calculate F · dr, C where F(x, y) = 2xyi + (y2 − x2)j (x2 + y2)2 and C is any positively oriented simple closed curve that encloses the origin.

Using Green's theorem we have:

int F.dr = int int d/dx ((y^2-x^2)/(x^2+y^2)^2) - d/dy (2xy/(x^2+y^2)^2) =

(2x^3 - 6xy^2) / (x^2+y^2)^3 - (2x^3 - 6xy^2) / (x^2+y^2)^3 = 0

Therefore:

int F.dr = 0

Step-by-step explanation:

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step-by-step explanation: umm..