# Matlab ICE

Create a Matlab function that does an adaptive trapezoidal rule. The function should take four arguments: the function whose integral is to be approximated; the left endpoint of the interval of integration; the right endpoint; and a tolerance for changes in the estimate of the integral. The last quantity is key. The function will approximate the integral with a simple, single-interval trapezoidal rule, and then again with a two-interval trapezoidal rule. It will compare the two values, and if the absolute value of the difference between them is smaller than the tolerance, then it declares victory.

Note that this function will use recursion. Care will be required to avoid mistakes of infinite recursion.

A solution for the
final is available.