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Today's calculation of Integral 669

Source: 1978 Mie University entrance exam

July 3, 2011
calculusintegrationfunctioncalculus computations

Problem Statement

Find the differentiable function defined in x>0x>0 such that ∫1f(x)f−1(t)dt=13(x32−8).{\int_1^{f(x)} f^{-1}(t)dt=\frac 13(x^{\frac {3}{2}}-8}).
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