Example 1.  Use Adaptive Simpson's rule to compute a numerical approximation to the integral  .  
Use the tolerances .  Compare with the analytic or "true value" of the integral.

Solution 1.

tol	0.001`	produces
tol	0.00001`	produces
tol	1.`*^-7	produces
true	value	is

Did the adapt subroutine behave as expected ?

The following graph illustrates the example.

(c) John H. Mathews 2003