Folks,

Find a simple closed curve with counter clockwise rotation that maximizes the value of

If I apply greens theoremI calculate ...?

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- Jan 11th 2012, 11:06 AMbugatti79Closed Curve Integral
Folks,

Find a simple closed curve with counter clockwise rotation that maximizes the value of

If I apply greens theoremI calculate ...? - Jan 11th 2012, 01:35 PMRidleyRe: Closed Curve Integral
Everything looks good except your answer. That integral does not evaluate to 1/2.

You want to maximize where . Setting reveals where f has its min and max. - Jan 11th 2012, 10:40 PMbugatti79Re: Closed Curve Integral
- Jan 11th 2012, 11:50 PMchisigmaRe: Closed Curve Integral
- Jan 12th 2012, 12:16 AMchisigmaRe: Closed Curve Integral
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...

(1)

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...

Kind regards

- Jan 12th 2012, 09:27 AMbugatti79Re: Closed Curve Integral