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Today's calculation of Integral 827

Source: 2012 Kyusyu University entrance exam/Mahematics, 2nd exam

July 1, 2012
calculusintegrationlimittrigonometrycalculus computations

Problem Statement

Find lim⁡n→∞∑k=0∞∫2kπ(2k+1)πxe−xsin⁡x dx.\lim_{n\to\infty}\sum_{k=0}^{\infty} \int_{2k\pi}^{(2k+1)\pi} xe^{-x}\sin x\ dx.
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