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Today's calculation of Integral 144

Source: Shizuoka University entrance exam 1978

August 28, 2006
calculusintegrationlimittrigonometrycalculus computations

Problem Statement

Evaluate lim⁡n→∞∫0π∣(x+πn)sin⁡nx∣ dx (n=1, 2, ⋯ ).\lim_{n\to\infty}\int_{0}^\pi \left|\left(x+\frac{\pi}{n}\right)\sin nx\right|\ dx\ (n=1,\ 2,\ \cdots).
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