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Today's calculation of Integral 886

Source: 2013 Nagoya City University entrance exam/Pharmacy

July 16, 2013
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

Find the functions f(x), g(x)f(x),\ g(x) such that
f(x)=exsin⁡x+∫0πug(u) duf(x)=e^{x}\sin x+\int_0^{\pi} ug(u)\ du g(x)=excos⁡x+∫0πuf(u) dug(x)=e^{x}\cos x+\int_0^{\pi} uf(u)\ du
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