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Math Help - Integral problem from Hardy book #2

  1. #1
    MHF Contributor Also sprach Zarathustra's Avatar
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    Integral problem from Hardy book #2

    I have no idea how to start to solve it.


    Thank you...
    Attached Thumbnails Attached Thumbnails Integral problem from Hardy book #2-47.png  
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  2. #2
    Senior Member roninpro's Avatar
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    The first thing that comes to mind is using force. Did you try it?
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  3. #3
    MHF Contributor chisigma's Avatar
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    Probably it is a particular application of gaussian quadrature...

    Gaussian Quadrature -- from Wolfram MathWorld

    The gaussian quadrature approximate a definite integral as...

    \displaystyle \int_{a}^{b} f(x)\cdot dx \approx \sum_{k=1}^{n} a_{k} \cdot f(x_{k}) (1)

    ... where the x_{k} are the zeroes of the Legendre polynomial of degree n. An interesting property of the gaussian quadrature is that the error vanishes if f(*) is a polynomial of degree less or equal to 2n-1, and that situation is achieved if n=3 and f(*) is a polynomial of degree 5 or less...

    Kind regards

    \chi \sigma
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