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Find integral using Gaussian Quadrature Method (numerical)

  1. Dec 5, 2009 #1
    1. The problem statement, all variables and given/known data

    approximate this integral: [tex]\oint[/tex] e^(-(x^2)) from 0 to 4 using
    Gaussian Quadrature with n = 3

    2. Relevant equations
    can be found at:


    3. The attempt at a solution
    n = 3
    coefficients: c(1) = c(3) = 5/9, c(2) = 8/9
    roots of a polynomial: xi = +/- (3/5)0.5, 0
    now I plugged it into the "change of interval" form of the formula (found in wikipedia) and I got an answer of 0.939335, which still seems to be "off", but at least better than using the composite trapezoid way. Is this number right? Because generally when I do this, I get numbers that are pretty much bang on, or at the very least get 2 digits correct!
  2. jcsd
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