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Today's calculation of Integral 832

Source: 2012 Osaka University of Education entrance exam, 2nd exam

July 3, 2012
calculusintegrationlimitlogarithmstrigonometrycalculus computations

Problem Statement

Find the limit lim⁡n→∞1nln⁡n∫π(n+1)π(sin⁡2t)(ln⁡t) dt.\lim_{n\to\infty} \frac{1}{n\ln n}\int_{\pi}^{(n+1)\pi} (\sin ^ 2 t)(\ln t)\ dt.
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