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Today's calculation of Integral 722

Source: 1993 Aichi Institute of Technology entrance exam

June 27, 2011
calculusintegrationfunctioncalculus computations

Problem Statement

Find the continuous function f(x)f(x) such that : ∫0xf(t)(∫0tf(t)dt)dt=f(x)+12\int_0^x f(t)\left(\int_0^t f(t)dt\right)dt=f(x)+\frac 12
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