- #1

- 92

- 0

## 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: x

_{i}= +/- (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!