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