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Today's calculation of Integral 284

Source: 1990 Tohoku University entrance exam

January 24, 2008
calculusintegrationfunctionlogarithmscalculus computations

Problem Statement

f(x) f(x) is a continuous function which takes positive values for x≥0. x\geq 0. Find f(x) f(x) such that \int_0^x f(t)dt\equal{}x\sqrt{f(x)} with f(1)\equal{}\frac{1}{2}.
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