Example 4.  Use the adaptive Simpson's rule to compute a numerical approximation to the integral    that we investigated in example 2.  
The long solution is obtained if you add a print statement to investigate the in between computations.  
This subroutine is pedagogical and is intended to help us understand what's happening in a recursive program.
You would probably not want to always print out the in between steps, so you might want to re-execute the first version for some of your work.

Solution 4.

Now investigate the "recursive path" the subroutine takes.

Now plot the intervals    where Simpson Rule was applied in the form  

  

(c) John H. Mathews 2004