MathDB
Today's calculation of Integral 751

Source:

September 7, 2011
calculusintegrationlimittrigonometrylogarithmscalculus computations

Problem Statement

Find lim⁡n→∞(1n∫0n(sin⁡2πx)ln⁡(x+n)dx−12ln⁡n).\lim_{n\to\infty}\left(\frac{1}{n}\int_0^n (\sin ^ 2 \pi x)\ln (x+n)dx-\frac 12\ln n\right).
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