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820

Part of 2012 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 820

Source: 1994 Seikei University entrance exam/Engineering

6/13/2012
Let PkP_k be a point whose xx-coordinate is 1+kn (k=1, 2, ⋯ , n)1+\frac{k}{n}\ (k=1,\ 2,\ \cdots,\ n) on the curve y=ln⁡xy=\ln x. For A(1, 0)A(1,\ 0), find the limit lim⁡n→∞1n∑k=1nAPk‾2.\lim_{n\to\infty} \frac{1}{n}\sum_{k=1}^{n} \overline{AP_k}^2.
calculusintegrationanalytic geometrylogarithmslimitcalculus computations