The two-point Gauss quadrature rule is an extension of the rapezoidal t rule approximation. Since the degree of fx is less than 2n-1 the Gaussian quadrature formula involving the weights and nodes obtained from applies. The midpoint rule is aone point rule because it only has one quadrature point.
This page is a tabulation of weights and abscissae for use in performing Legendre-Gauss quadrature integral approximation which tries to solve the following function by picking approximate values for n w i and x iWhile only defined for the interval -11 this is actually a universal function because we can convert the limits of integration for.
An approximate formula for the calculation of a definite integral. For example if you want to know what are the values of xand cfor a 2-point formula on 11 try the following. It follows that the Gaussian quadrature method if we choose the roots of the Legendre polynomials for the n abscissas will yield exact results for any polynomial of degree less than 2n and will yield a good approximation to the integral if Sx is a polynomial representation of a general function fx obtained by fitting a. See numerical integration for more on quadrature rules An n-point Gaussian quadrature rule named after Carl Friedrich Gauss is a quadrature rule constructed to yield an exact result.