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Today's calculation of Integral 381

Source: 1993 Musashi Institute of Technogy entrance exam

October 18, 2008
calculusintegrationfunctiontrigonometrycalculus computations

Problem Statement

A function f(x) f(x) is defined as follows for x≥0 x\geq 0. f(x) \equal{} \sin \left(\frac {n\pi}{4}\right)\sin x\ (n\pi \leq x < (n \plus{} 1)\pi)\ (n \equal{} 0,\ 1,\ 2,\ \cdots). Evaluate ∫0100πf(x) dx \int_0^{100\pi} f(x)\ dx.
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