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Today's calculation of Integral 819

Source: 2012 Waseda University of Education enatrance exam Prob. 1A

May 27, 2012
calculusintegrationtrigonometrylimitcalculus computations

Problem Statement

For real numbers a, ba,\ b with 0≤a≤π, a<b0\leq a\leq \pi,\ a<b, let I(a, b)=∫abe−xsin⁡x dx.I(a,\ b)=\int_{a}^{b} e^{-x} \sin x\ dx.
Determine the value of aa such that lim⁡b→∞I(a, b)=0.\lim_{b\rightarrow \infty} I(a,\ b)=0.
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