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Math Help - integration help,

  1. #1
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    integration help,

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


    I know i have to split into partial fractions, but not sure how to go from there
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  2. #2
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    Re: integration help,

    Have you determined the partial fraction decomposition? Once you do, then the integration is straightforward. Are you familiar with the cover-up method?
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  3. #3
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    Re: integration help,

    I have I got  \int^1_0 \frac{-1}{x+1} + \frac{1}{x+2}

    I than get,  \int^1_0 -ln(x+1) + ln(x+2)

    and I dont know how to go from here, i dont even know if am right
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  4. #4
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    Re: integration help,

    That's the correct partial fraction decomposition. In the second line, instead of an integral sign, you want -ln(x+1)+ln(x+2) evaluated from 0 to 1, so it's -ln(1+1)+ln(1+2)+ln(0+1)-ln(0+2). Now you can combine the logarithms to get k.

    - Hollywood
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  5. #5
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    Re: integration help,

    Quote Originally Posted by Tweety View Post
    I have I got  \int^1_0 \frac{-1}{x+1} + \frac{1}{x+2}

    I than get,  \int^1_0 -ln(x+1) + ln(x+2)

    and I dont know how to go from here, i dont even know if am right
    Let me just touch it up a bit:

    \int^1_0 \frac{-1}{(x+1)(x+2)} \ dx

    = \int^1_0 \left( \frac{-1}{x+1} + \frac{1}{x+2} \right) dx

    = \int^1_0 \frac{-1}{x+1} \ dx +  \int^1_0  \frac{1}{x+2} \ dx

    = \left\ -ln(x+1)\right]_0^1 + \left\ ln(x+2)\right]_0^1

    And from there:

    Spoiler:

    = \left\{ [-ln((1)+1)] - [-ln((0)+1)] \right\} + \left\{ [ln((1)+2)] - [ln((0)+2)] \right\}

    = \left\{ [-ln(2)] - [-ln(1)] \right\} + \left\{ [ln(3)] - [ln(2)] \right\}

    = -ln(2) + ln(1) + ln(3) - ln(2)

    = ln(1) + ln(3)

    = (0) + ln(3)

    = ln(3)
    Last edited by johnsomeone; October 8th 2012 at 08:21 AM.
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  6. #6
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    Re: integration help,

    Johnsomeone - could you please check the third and fourth lines of your spoiler?

    Thanks,
    Hollywood
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  7. #7
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    Re: integration help,

    My spoiler is spoiled!

    From -ln(2) + ln(1) + ln(3) - ln(2) to ln(1) + ln(3)? Not my best bit of calculation.

    It should be

    -ln(2) + ln(1) + ln(3) - ln(2) = ln(3)-2ln(2) = ln(3) - ln(2^2) = ln(3/4).

    Thanks for catching my error.
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