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Today's calculation of Integral 186

Source: Tohoku University entrance exam/Science 2007

February 28, 2007
calculusintegrationlimitcalculus computations

Problem Statement

For a>0,a>0, find lim⁡a→∞a−(32+n)∫0axn1+x dx (n=1, 2, ⋯ ).\lim_{a\to\infty}a^{-\left(\frac{3}{2}+n\right) }\int_{0}^{a}x^{n}\sqrt{1+x}\ dx\ (n=1,\ 2,\ \cdots).
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