Example 2.  Numerically approximate the integral  [Graphics:Images/SimpsonRuleMod_gr_78.gif]  by using Simpson's rule with  m = 10, 20, 40, 80,  and 160.

Solution 2.

We will use the subroutine for the solution.

[Graphics:../Images/SimpsonRuleMod_gr_79.gif]

[Graphics:../Images/SimpsonRuleMod_gr_80.gif]
[Graphics:../Images/SimpsonRuleMod_gr_81.gif]
[Graphics:../Images/SimpsonRuleMod_gr_82.gif]


[Graphics:../Images/SimpsonRuleMod_gr_83.gif]
[Graphics:../Images/SimpsonRuleMod_gr_84.gif]
[Graphics:../Images/SimpsonRuleMod_gr_85.gif]


[Graphics:../Images/SimpsonRuleMod_gr_86.gif]
[Graphics:../Images/SimpsonRuleMod_gr_87.gif]
[Graphics:../Images/SimpsonRuleMod_gr_88.gif]


[Graphics:../Images/SimpsonRuleMod_gr_89.gif]
[Graphics:../Images/SimpsonRuleMod_gr_90.gif]
[Graphics:../Images/SimpsonRuleMod_gr_91.gif]


[Graphics:../Images/SimpsonRuleMod_gr_92.gif]
[Graphics:../Images/SimpsonRuleMod_gr_93.gif]
[Graphics:../Images/SimpsonRuleMod_gr_94.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004