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Math Help - integration problem

  1. #1
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    integration problem

    can anybody help me with this integral ?

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  2. #2
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    Hello, rbenito!

    I got a different answer . . .


    \int^{\infty}_0 a\,x\,e^{-a}\,dx

    Integrate by parts . . .

    . . \begin{array}{ccccccc}u & = & x & \quad & dv & = & ae^{-ax}dx \\<br />
du & = & dx & \quad & v & = & -e^{-ax}\end{array}

    We have: . -xe^{-ax} + \int^{\infty}_0\!\! e^{-ax}dx \;\;=\;\;-xe^{-ax} - \frac{1}{a}e^{-ax}\,\bigg]^{\infty}_0 \;\;=\;\;-\frac{e^{-ax}}{a}(ax + 1)\,\bigg]^{\infty}_0

    . . = \;\lim_{t\to\infty}\left[-\frac{ax+1}{ae^{ax}}\right]^t_0 \;= \;\lim_{t\to\infty}\left[-\frac{at+1}{ae^{at}} - \left(-\frac{1}{a}\right)\right] \;=\;0 - \left(-\frac{1}{a}\right) \;=\;\frac{1}{a}<br />

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  3. #3
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    Hey Soroban.

    I believe you're right. I see my mistake.

    After looking at it again, I get the same.
    Last edited by galactus; September 15th 2007 at 02:40 PM.
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