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Thread: Help with and improper integral!

  1. #1
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    Help with and improper integral!

    I need help to figure out how can i resolve this improper integral, i don't know what to do with the absolute value:


    ∫e^(-lyl) <--- Where lyl is the absolute value of "y", and evaluated from -∞ to
    -∞
    There is also a photo attached of the integral. Thanks!
    Attached Thumbnails Attached Thumbnails Help with and improper integral!-improper-int.jpg  
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  2. #2
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    Re: Help with and improper integral!

    $\begin{align*}
    &\displaystyle \int_{-\infty}^\infty e^{-|y|}~dy = \\

    &\int_{-\infty}^0 e^{-|y|}~dy +\int_{0}^\infty e^{-|y|}~dy = \\

    &\int_{-\infty}^0 e^y~dy + \int_0^\infty e^{-y}~dy

    \end{align*}$

    can you finish it?
    Thanks from HallsofIvy
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  3. #3
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    Re: Help with and improper integral!

    Always split integrals with absolute values at the point the interior expression changes sign.
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  4. #4
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    Re: Help with and improper integral!

    Quote Originally Posted by romsek View Post
    $\begin{align*}
    &\displaystyle \int_{-\infty}^\infty e^{-|y|}~dy = \\

    &\int_{-\infty}^0 e^{-|y|}~dy +\int_{0}^\infty e^{-|y|}~dy = \\

    &\int_{-\infty}^0 e^y~dy + \int_0^\infty e^{-y}~dy

    \end{align*}$

    can you finish it?
    Yeah man, thank you so much!
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