Given the length L of a curve going two given point $(a,\alpha)$, $(b,\beta)$ find the equation of the curve so that the curve together with the interval $[a,b]$ encloses the largest area. Am I correct in thinking this is Dido's problem? Is it possible to use Green's theorem to find the equation?
Calculus of Variation (Dido's Problem?)
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calculus-of-variations