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Today's calculation of Integral 180

Source: Waseda university entrance exam 2007

February 16, 2007
calculusintegrationgeometrytrigonometrylimitcalculus computations

Problem Statement

Let ana_{n} be the area surrounded by the curves y=e−xy=e^{-x} and the part of y=e−x∣cos⁡x∣, (n−1)π≤x≤nπ (n=1, 2, 3, ⋯ ).y=e^{-x}|\cos x|,\ (n-1)\pi \leq x\leq n\pi \ (n=1,\ 2,\ 3,\ \cdots). Evaluate lim⁡n→∞(a1+a2+⋯+an).\lim_{n\to\infty}(a_{1}+a_{2}+\cdots+a_{n}).
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