553

Part of 2010 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 553

Source: 2010 Doshisya University entrance exam/Life Science

Find the continuous function such that f(x)\equal{}\frac{e^{2x}}{2(e\minus{}1)}\int_0^1 e^{\minus{}y}f(y)dy\plus{}\int_0^{\frac 12} f(y)dy\plus{}\int_0^{\frac 12}\sin ^ 2(\pi y)dy.

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