# a problem about integral

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• January 5th 2012, 03:36 AM
mami
a problem about integral
$\lim_{n\to\infty}\int_{0}^{\sqrt{n}}\left(1-\frac{\left x^2\right}{n}\right )^{n}dx$

i couldn't tackle it
thanks for now.
• January 5th 2012, 03:53 AM
girdav
Re: a problem about integral
Do you know the dominated convergence theorem?
• January 5th 2012, 11:03 AM
FernandoRevilla
Re: a problem about integral
It can be useful the substitution $t=x/\sqrt{n}$, so $\int_{0}^{\sqrt{n}}(1-x^2/n)^n\;dx=\sqrt{n}\int_{0}^{1}(1-t^2)^n\;dt$ .