Question: Suppose that f is a real, continuously differentiable function on [0, 1] with f(0) : f (1) = 0, and %3D 1 = 1.

Suppose that f is a real, continuously differentiable function on [0, 1]

Suppose that f is a real, continuously differentiable function on [0, 1] with f(0) : f (1) = 0, and %3D 1 = 1. Prove that 1 = - xf(x)f'(x)dx and 1 1 x[f(x)]*dx

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