# 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.

Assignment 6 is posted.

The midterm exam will take place on Friday,
12 October. As always, you are permitted any paper
notes you find useful, but no electronic devices are
allowed. The test is cumulative, but emphasizes
the material covered in the last fours weeks.
A sample exam is
available.

You need to install
Matlab
on your computer by Wednesday.
You do not need Simulink or any particular toolboxes, though
you might find the Symbolic toolbox useful at some time
in the future (not in this class).