Find a simple closed curve with counter clockwise rotation that maximizes the value of
If I apply greens theoremI calculate ...?
Because is 'invariant to rotation' we can suppose that C is a circle centered in the origin and with radious R, so that we have to find the R that maximizes the contour integral. We can write...
If we compute the derivative of the (1) respect to R we find that it vanishes for so that R=1 is the requested value and the curve is [effectively...] the unity circle...