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Thread: a problem about integral

  1. January 5th 2012, 03:36 AM #1
    mami
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    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.
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  2. January 5th 2012, 03:53 AM #2
    girdav
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    Re: a problem about integral

    Do you know the dominated convergence theorem?
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  3. January 5th 2012, 11:03 AM #3
    FernandoRevilla
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    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 .
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