Use a Lagrange multiplier to find the curve (x(y)) of length (L=pi) on the interval ([0,1]) which

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Use a Lagrange multiplier to find the curve \(x(y)\) of length \(L=\pi\) on the interval \([0,1]\) which maximizes the integral \(I=\int_{0}^{1} y(x) d x\) and pass through the points \((0,0)\) and \((1,0)\).

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