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Thread: partial fraction integration, please check my working out

  1. #1
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    partial fraction integration, please check my working out

    . What is the exact value of ? Give your answer as a fraction or whole number.

    I split the fraction, into two fractions, using partial fractions method, to get

    $\displaystyle \int^2_0 \frac{2}{x+4} -\frac{2}{x+5} $

    = $\displaystyle ln(x+4) - ln(x+5) $

    $\displaystyle ln\frac{x+4}{x+5} $

    x=2
    x=0

    $\displaystyle ln\frac{6}{7} - ln\frac{4}{5} $


    $\displaystyle ln \frac{30}{28} = 0.06899 $

    is the the value of k?

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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: partial fraction integration, please check my working out

    You made one error in your integration, you neglected the 2 in the numerator of your integrands, which just means you need to square 30/28 = 15/14 to get the value of k.
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  3. #3
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    Re: partial fraction integration, please check my working out

    Quote Originally Posted by MarkFL2 View Post
    You made one error in your integration, you neglected the 2 in the numerator of your integrands, which just means you need to square 30/28 = 15/14 to get the value of k.
    oh yes thank you, so the value of k is 1.071?
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: partial fraction integration, please check my working out

    No, you wind up with:

    $\displaystyle 2\ln\left(\frac{15}{14} \right)=\ln(k)$

    $\displaystyle \ln\left(\left(\frac{15}{14} \right)^2 \right)=\ln(k)$

    And so:

    $\displaystyle k=\left(\frac{15}{14} \right)^2=\frac{225}{196}$
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