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Today's calculation of Integral 329

Source: 2008 Hokkaido University entrance exam/Science

May 29, 2008
calculusintegrationfunctioncalculus computations

Problem Statement

Let f(x), g(x) f(x),\ g(x) be continuous functions defined in the range of 0≤x≤1 0\leq x\leq 1. (1) Find f(x) f(x) such that f(x)\equal{}\int_0^1 e^{x\plus{}t}f(t)\ dt. (2) Find g(x) g(x) such that g(x)\equal{}\int_0^1 e^{x\plus{}t}g(t)\ dt\plus{}x.
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