Example 1.  Numerically approximate the integral  [Graphics:Images/SimpsonRuleMod_gr_61.gif]  by using Simpson's rule with  m = 1, 2, 4, and 8.

Solution 1.

[Graphics:../Images/SimpsonRuleMod_gr_62.gif]

[Graphics:../Images/SimpsonRuleMod_gr_63.gif]

[Graphics:../Images/SimpsonRuleMod_gr_64.gif]

We will use simulated hand computations for the solution.

[Graphics:../Images/SimpsonRuleMod_gr_65.gif]

[Graphics:../Images/SimpsonRuleMod_gr_66.gif]
[Graphics:../Images/SimpsonRuleMod_gr_67.gif]
[Graphics:../Images/SimpsonRuleMod_gr_68.gif]


[Graphics:../Images/SimpsonRuleMod_gr_69.gif]
[Graphics:../Images/SimpsonRuleMod_gr_70.gif]
[Graphics:../Images/SimpsonRuleMod_gr_71.gif]


[Graphics:../Images/SimpsonRuleMod_gr_72.gif]
[Graphics:../Images/SimpsonRuleMod_gr_73.gif]
[Graphics:../Images/SimpsonRuleMod_gr_74.gif]


[Graphics:../Images/SimpsonRuleMod_gr_75.gif]
[Graphics:../Images/SimpsonRuleMod_gr_76.gif]
[Graphics:../Images/SimpsonRuleMod_gr_77.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004