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Math Help - Integration trouble!

  1. #1
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    Thumbs up Integration trouble!

    Hey people, I know this may seem trivial but i'm having some trouble integrating a function. I have always been weak with integration but this one has a constant and is baffling me! the function to be integrated is:

    f(x) = x^2.e^(-Px)

    I would really appreciate if anyone could help me solve this one!

    Thanks,
    Watto
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  2. #2
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    Quote Originally Posted by watto23 View Post
    Hey people, I know this may seem trivial but i'm having some trouble integrating a function. I have always been weak with integration but this one has a constant and is baffling me! the function to be integrated is:

    f(x) = x^2.e^(-Px)

    I would really appreciate if anyone could help me solve this one!

    Thanks,
    Watto
    You need to use integration by parts.

    \int{u\,dv} = u\,v - \int{v\,du}


    So for \int{x^2e^{-px}\,dx}

    you let u = x^2 so that du = 2x

    and dv = e^{-px} so that v = -\frac{e^{-px}}{p}.


    Therefore

    \int{x^2e^{-px}\,dx} = -\frac{x^2e^{-px}}{p} - \int{-\frac{2x\,e^{-px}}{p}\,dx}

     = -\frac{x^2e^{-px}}{p} + \frac{2}{p}\int{x\,e^{-px}\,dx}.


    Now you need to use integration by parts again.

    Let u = x so that du = 1

    Let dv = e^{-px} so that v = -\frac{e^{-px}}{p}.


    So -\frac{x^2e^{-px}}{p} + \frac{2}{p}\int{x\,e^{-px}\,dx} = -\frac{x^2e^{-px}}{p} + \frac{2}{p}\left(-\frac{x\,e^{-px}}{p} - \int{-\frac{1e^{-px}}{p}\,dx}\right)

     = -\frac{x^2e^{-px}}{p} - \frac{2x\,e^{-px}}{p^2} + \frac{2}{p^2}\int{e^{-px}\,dx}

     = -\frac{x^2e^{-px}}{p} - \frac{2x\,e^{-px}}{p^2} - \frac{2e^{-px}}{p^3} + C.
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  3. #3
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    Thumbs up

    nice one buddy thanks for the quick reply
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  4. #4
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    Thumbs up

    Hey having some more trouble with this problem,

    I was asked to numerically integrate the function:

    f(x) = x^2.e^(-Px)

    between the limits 0 and 2*pi where p=3

    On a computer program called MATLAB I have done so using the trapezium and simpsons rule and evaluated the integral as 0.0741 for both with a sufficient number of intervals.

    however the proof above seems correct but it gives me an extremely small number for the integral due to e^(-Px) being roughly e^-18.

    Can anyone shed some light into where i may have gone wrong?
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