Theoretical integralclosed smooth contour

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itsagoal89
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compute the integral of ...i can't find the integral symbol, but is the standard integral sign with a circle in the middle of it and a c to the bottom right of it.

F*dr where C is an arbitrary closed smooth contour that does not enclose the origin.
 
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where Vector Field F=(-y/(x^2+y^2),x/(x^2+y^2)