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Today's calculation of Integral 665

Source:

January 12, 2011
calculusintegrationlimittrigonometrycalculus computations

Problem Statement

Find lim⁡n→∞∫0πx∣sin⁡2nx∣dx (n=1, 2, ⋯ )\lim_{n\to\infty} \int_0^{\pi} x|\sin 2nx| dx\ (n=1,\ 2,\ \cdots).
1992 Japan Women's University entrance exam/Physics, Mathematics
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