Question: (a) Find the curve y(x) that passes through the endpoints (0, 0) and (1, 1) and minimizes the functional I[y] = 1/0 [(dy/dx) 2

(a) Find the curve y(x) that passes through the endpoints (0, 0) and (1, 1) and minimizes the functional I[y] = ∫1/0 [(dy/dx) 2 – y2] dx.
(b) What is the minimum value of the integral?
(c) Evaluate I[y] for a straight line y = x between the points (0, 0) and (1, 1).

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