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Find integral using Gaussian Quadrature Method (numerical)

  • Thread starter war485
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Homework Statement



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

Homework Equations


can be found at:

http://en.wikipedia.org/wiki/Gaussian_quadrature

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!
 

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