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Today's calculation of Integral 158

Source: Tokyo Institute of Technology entrance exam 1994

October 6, 2006
calculusintegrationtrigonometrylimitcalculus computations

Problem Statement

(1) Evaluate the definite integral ∫0πe−xsin⁡xdx.\int_{0}^{\pi}e^{-x}\sin x dx. (2) Find the limit lim⁡n→∞∫0nπe−x∣sin⁡x∣dx.\lim_{n\to\infty}\int_{0}^{n\pi}e^{-x}|\sin x| dx.
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