Adaptive Methods

Adaptive methods are used to estimate the integral of a function on a closed and bounded interval. The basic idea is to take smaller subintervals in regions where the function changes significantly and larger subintervals in regions where the function doesn't change significantly. What is significant depends on the quadrature technique involved, for Simpson's rule, if the function is nearly cubic (or quadratic, or linear, or constant) then the function doesn't change significantly from being cubic and a large interval can be used.