Gauss-Legendre quadrature considers the simplest case of uniform weighting: \(w(x) = 1\). Hence,
this method is useful for functions \(f(x)\) which can be approximated by polynomials. Therefore,
this method is for finding the integral
where \(f(x)\) can be well approximated by a polynomial.
For finding an integral over the interval [a,b], that is,
change of variable can be used.
Generating evaluation points is done by finding roots of Legendre polynomials, hence the name of
this method. Finding the roots has to be done numerically, but the coefficients can be computed
directly. Since the roots lie within the open interval (-1, 1), the formulae are open integration