Question: Consider a string of fixed length l that has one end fixed at the point, (x = a, y = 0), and the other end

Consider a string of fixed length l that has one end fixed at the point, (x = a, y = 0), and the other end fixed at the point (x = a, y = 0). What shape y(x) should the string take so that the area enclosed between it and the x-axis is maximized? Though this is intuitively obvious, please use the calculus of variations to prove it. This problem is similar to problem 6.22 in Taylor

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