Example 3.  Find the analytic value of the integral  [Graphics:Images/Simpson38RuleMod_gr_93.gif]  (i.e. find the "true value").   

Solution 3.

The integral of  [Graphics:../Images/Simpson38RuleMod_gr_94.gif]  can be determined.

[Graphics:../Images/Simpson38RuleMod_gr_95.gif]
[Graphics:../Images/Simpson38RuleMod_gr_96.gif]

The value of the definite integral

[Graphics:../Images/Simpson38RuleMod_gr_97.gif]
[Graphics:../Images/Simpson38RuleMod_gr_98.gif]


[Graphics:../Images/Simpson38RuleMod_gr_99.gif]
[Graphics:../Images/Simpson38RuleMod_gr_100.gif]

[Graphics:../Images/Simpson38RuleMod_gr_101.gif]
[Graphics:../Images/Simpson38RuleMod_gr_102.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004