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Today's calculation of Integral 803

Source: 2012 Yokohama National University /Science, 2nd exam # 1

March 13, 2012
calculusintegrationlimitlogarithmsfactorialcalculus computations

Problem Statement

Answer the following questions:
(1) Evaluate ∫−11(1−x2)e−2xdx.\int_{-1}^1 (1-x^2)e^{-2x}dx.
(2) Find lim⁡n→∞{(2n)!n!nn}1n.\lim_{n\to\infty} \left\{\frac{(2n)!}{n!n^n}\right\}^{\frac{1}{n}}.
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