# 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.

The "final exam" for this course will take place
at 8:00 AM on Tuesday, 12 December. This will be an ordinary
50 minute test. It will be comprehensive, but weighted toward
the latter half of the semester. As always, paper notes will
be permitted, but no electronic devices will be allowed.
A sample exam is available.

A
Solution example is available
for the quiz. The solution to
Test 1 is still available too.

The ultimate assignment is posted.