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Thread: Integration by splitting the numerator

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    Integration by splitting the numerator

    Integral of (5-x^2)dx / sqrt(3-2x-x^2)

    By splitting the numerator, thanks for the help!
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    Re: Integration by splitting the numerator

    Quote Originally Posted by pikachu975 View Post
    Integral of (5-x^2)dx / sqrt(3-2x-x^2)

    By splitting the numerator, thanks for the help!










    Last edited by InteGrand; 14 Feb 2017 at 5:44 PM.

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    Re: Integration by splitting the numerator

    Quote Originally Posted by InteGrand View Post










    Thanks again for the help, can you please show me how to write the (5-x^2) in the form you stated, because I don't quite understand it. Thanks!
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    Re: Integration by splitting the numerator

    Quote Originally Posted by pikachu975 View Post
    Thanks again for the help, can you please show me how to write the (5-x^2) in the form you stated, because I don't quite understand it. Thanks!




    Last edited by InteGrand; 14 Feb 2017 at 6:17 PM.
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    Re: Integration by splitting the numerator

    Quote Originally Posted by InteGrand View Post




    I tried it and got a = 1, b = -1, c = 0, but I don't think it's right

    5-x^2 = -ax^2 - 2x (a+b) + (3a-2b+c)
    So a = 1 by equating coefficients
    a+b = 0, so b = -1
    3a-2b+c = 5
    3 + 2 + c = 5
    c = 0

    Did I do something wrong?
    2016 HSC (Accelerated)
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    2017 HSC
    // Biology // Physics // Maths Extension 1 // Maths Extension 2 // English Advanced //

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    Re: Integration by splitting the numerator

    Quote Originally Posted by pikachu975 View Post
    I tried it and got a = 1, b = -1, c = 0, but I don't think it's right

    5-x^2 = -ax^2 - 2x (a+b) + (3a-2b+c)
    So a = 1 by equating coefficients
    a+b = 0, so b = -1
    3a-2b+c = 5
    3 + 2 + c = 5
    c = 0

    Did I do something wrong?

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    Re: Integration by splitting the numerator

    Hey, here's my solution. It took me a while tho...





    Note 10 attempts at editing it to get the equation to be valid... rip
    Last edited by BenHowe; 14 Feb 2017 at 8:39 PM.
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    1st Year BAppFinBActStud @ MQ

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