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Math Help - Integration

  1. #1
    ixi
    ixi is offline
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    Oct 2007
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    Integration

    The question is:

    The integration of e^(-abs (x)) from -infinitiy to + infinity



    The absolute before the x is throwing me off...

    I got

    -e^(-abs(x)) from -infinitiy to + infinity

    i graphed it but doesn't it go to 0?

    so would the answer be 0?


    thanks
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  2. #2
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    \int_{-\infty}^\infty e^{-|x|}dx=\int_{-\infty}^0 e^{-|x|}dx+\int_{0}^\infty e^{-|x|}dx

    Now when x\in(-\infty,0], |x|= -x, so -|x|= -(-x)=x

    And when x\in[0,\infty), |x|=x and so -|x|=-x

    So therefore \int_{-\infty}^0 e^{-|x|}dx+\int_{0}^\infty e^{-|x|}dx=\int_{-\infty}^0 e^{x}dx+\int_{0}^\infty e^{-x}dx

    =1+1=2 if you need help with the integration let me know
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