The numerical integration methods described so far are based on a rather simple choice of evaluation points

for the function f(x). They are particularly suited for regularly tabulated data, such as one might measure in a

laboratory, or obtain from computer software designed to produce tables. If one has the freedom to choose

the points at which to evaluate f(x), a careful choice can lead to much more accuracy in evaluating the

integral in question. We shall see that this method, called Gaussian or Gauss-Legendre integration, has one

significant further advantage in many situations. In the evaluation of an integral on the interval to , it is