Example 1.  Numerically approximate the integral  [Graphics:Images/Simpson38RuleMod_gr_59.gif]  by using Simpson's 3/8 rule with  m = 1, 2, 4.

Solution 1.

[Graphics:../Images/Simpson38RuleMod_gr_60.gif]

[Graphics:../Images/Simpson38RuleMod_gr_61.gif]

[Graphics:../Images/Simpson38RuleMod_gr_62.gif]

We will use simulated hand computations for the solution.

[Graphics:../Images/Simpson38RuleMod_gr_63.gif]

[Graphics:../Images/Simpson38RuleMod_gr_64.gif]
[Graphics:../Images/Simpson38RuleMod_gr_65.gif]
[Graphics:../Images/Simpson38RuleMod_gr_66.gif]


[Graphics:../Images/Simpson38RuleMod_gr_70.gif]
[Graphics:../Images/Simpson38RuleMod_gr_71.gif]
[Graphics:../Images/Simpson38RuleMod_gr_72.gif]


[Graphics:../Images/Simpson38RuleMod_gr_73.gif]
[Graphics:../Images/Simpson38RuleMod_gr_74.gif]
[Graphics:../Images/Simpson38RuleMod_gr_75.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004