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Math Help - improper integral

  1. #1
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    improper integral

    evaluate the improper integral :

    \int_0^\infty{e(e^{-x}) \,dx}<br />
    Last edited by mr fantastic; May 3rd 2009 at 05:42 PM. Reason: Fixed latex
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  2. #2
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    Quote Originally Posted by fastman390 View Post
    evaluate the improper integral :

    <br />
\int_{0}^{\infty}e(e^{-x})dx<br />
    If this is what you mean

    <br />
\int_{0}^{\infty} e(e^{-x})dx<br />

    Then

    \lim_{b \to \infty} \int_{0}^{b} e(e^{-x})dx=\lim_{b \to \infty} e (-e^{-x})\bigg|_{0}^{b}=

    \lim_{b \to \infty} -e\cdot e^{-b}+e\cdot e^{0} =e
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