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Math Help - integration using partial fraction please can can someone check my working

  1. #1
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    integration using partial fraction please can can someone check my working

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





     \int^3_0 \frac{1}{(x+4)(x+5)}

    I have spilt this into partial fractions, and got

     1 = A(x+5) + B(x+4)

    which gives
    A=1
    B=-1

    so I have

     \int^3_0 \frac{1}{x+4} -\frac{1}{x+5}

    so now integrating i get

     ln(x+4)-ln(x+5)

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

    I than evaluate this answer from 3-0 and i get  ln\frac{7}{8} - ln\frac{4}{5}

    so I get 0.0936
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  2. #2
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    Re: integration using partial fraction please can can someone check my working

    \ln(7/8) - \ln(4/5) = \ln(7/8 \div 4/5) = \ln(35/32) \approx 0.0896
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  3. #3
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    Re: integration using partial fraction please can can someone check my working

    According to your original post, the question was "What is the exact value of k? Give your answer as a fraction or whole number". ln(7/8)- ln(4/5)= ln((7/8)(5/4))= ln(35/32).

    Don't forget what the problem asked while doing the work! Your answer to this question should be "k= 35/32".
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  4. #4
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    Re: integration using partial fraction please can can someone check my working

    Tahnk you, but the correct answer is 1.09357, I dont know where i went wrong
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  5. #5
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    Re: integration using partial fraction please can can someone check my working

    Quote Originally Posted by Tweety View Post
    Tahnk you, but the correct answer is 1.09357, I dont know where i went wrong
    after integration you end up with
    0.0896=\ln(k)
    this should give you k = 1.09357
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  6. #6
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    Re: integration using partial fraction please can can someone check my working

    You might notice that 35/32 = 1.09375. I'll bet the 7 and 5 got reversed somewhere, so HallsofIvy's answer is exactly correct, just in a fraction instead of a decimal.

    - Hollywood
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