Gauss-Legendre quadrature

In numerical analysis, Gauss-Legendre quadrature is a form of Gaussian quadrature for approximating the definite integral of a function. The lead gives the rule for integrating over the interval from minus one to one, where the integral is approximated by a weighted sum of function values at chosen points. Because it belongs to the Gaussian quadrature family, the points and weights are not equally spaced but are chosen to make the approximation accurate, and the interval from minus one to one is the standard form to which other intervals are rescaled.