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Please answer fully with details. Please show your wok and explain your reasoning. Will like if work is carefully thought out and unique. (12 points)

Please answer fully with details. Please show your wok and explain your reasoning. Will like if work is carefully thought out and unique.

(12 points) Find the admissible curve y() which minimizes subject to the boundary conditions y(0) = y(1) = 0 and the integral side condition J (y) = / y dx = 1

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