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36. Pro +72 37. (a) If f: [0, 1] R and f f(t)dt = f f(t)dt, Vr = [0, 1], then show that f(z)

36. Pro +72 37. (a) If f: [0, 1] R and f f(t)dt = f f(t)dt, Vr = [0, 1], then show that f(z) = 0, V = [0, 1]. (b) Suppose f(x) > 0, f(x) is continuous on [a, b], and f f(x) dx = 0. Prove that f(x) = 0 for all x [a, b].

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