Example 1.  Use the 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.

1 (a). Plot the function over the interval  [0, 1.25].

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

(c) John H. Mathews 2004