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Math Help - Quadrature formula

  1. #1
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    Quadrature formula

    Question: "Determine constants a, b, c, d, e that will produce a quadrature formula

    \int_{-1}^{1}f(x)dx=af(-1)+bf(0)+cf(1)+df'(-1)+ef'(1)

    that has degree of precision 4"

    Some background information: degree of precision of a quadrature formula is the largest positive integer n such that the formula is exact for x^k for each k = 0,1, ... , n.

    I'm not sure about this problem... I think d and e are 0 because a quadrature formula is given by constants times certain values f(x) at different x's. ie. the quadrature formula is:

    \int_{a}^{b} f(x) dx \approx \sum_{i=0}^{n} a_{i} f(x_{i})

    Any suggestions?
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  2. #2
    Grand Panjandrum
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    Re: Quadrature formula

    Quote Originally Posted by limddavid View Post
    Question: "Determine constants a, b, c, d, e that will produce a quadrature formula

    \int_{-1}^{1}f(x)dx=af(-1)+bf(0)+cf(1)+df'(-1)+ef'(1)

    that has degree of precision 4"

    Some background information: degree of precision of a quadrature formula is the largest positive integer n such that the formula is exact for x^k for each k = 0,1, ... , n.

    I'm not sure about this problem... I think d and e are 0 because a quadrature formula is given by constants times certain values f(x) at different x's. ie. the quadrature formula is:

    \int_{a}^{b} f(x) dx \approx \sum_{i=0}^{n} a_{i} f(x_{i})

    Any suggestions?
    You have a set of linear equations:

    \int_{-1}^{1}dx=a+b+c

    \int_{-1}^{1}x dx=a(-1)+b(0)+c(1)+d+e

    \int_{-1}^{1}x^2dx=a(-1)^2+b(0)^2+c(1)^2+2d(-1)+2e(1)

    etc

    which you can then solve for a,b,c,d,e

    CB
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