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158

Part of 2006 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 158

Source: Tokyo Institute of Technology entrance exam 1994

10/6/2006
(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.
calculusintegrationtrigonometrylimitcalculus computations