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Today's calculation of Integral 461

Source: 2009 Ohita University entrance exam/Medical

June 27, 2009
calculusintegrationlimitlogarithmsinequalitiescalculus computations

Problem Statement

Let I_n\equal{}\int_0^{\sqrt{3}} \frac{1}{1\plus{}x^{n}}\ dx\ (n\equal{}1,\ 2,\ \cdots). (1) Find I1, I2 I_1,\ I_2. (2) Find lim⁡n→∞In \lim_{n\to\infty} I_n.
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