Let C be a smooth simple closed curve in the xy-plane (oriented counter-clockwise), and consider the differential 1-form =-12ydx12xdy. The line integral C yields a number that depends in some way on the curve C.(a) Calculate this line integral for a circle of arbitrary radius R>0 centered at the origin. Do this by "brute force", by parametrizing the circle and converting the line integral into an ordinary integral.(b) Using you answer from (a) as a hint, make a conjecture about how the value of the line integral above is related to the curve C. Then prove your conjecture is true in general for any curve C.