Problem 3776

Problems in Mathematical Analysis · 7.2

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Problem 3776

By interchanging the integral sign with the limit sign, compute the integral

∫0+∞e−x2 dx=∫0+∞lim⁡n→∞[(1+x2n)−n]dx. \int _{0}^{+\infty }e^{-x^{2}}\, dx=\int _{0}^{+\infty }\lim _{n \to \infty }\left[\left(1+\dfrac {x^{2}}{n}\right)^{-n}\right]dx .
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Problem 3776.1
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Problem 3776.2
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