Example 3.  Find the analytic value of the integral  [Graphics:Images/MidpointRuleMod_gr_84.gif]  (i.e. find the "true value").   

Solution 3.

[Graphics:../Images/MidpointRuleMod_gr_85.gif]
[Graphics:../Images/MidpointRuleMod_gr_86.gif]


[Graphics:../Images/MidpointRuleMod_gr_87.gif]
[Graphics:../Images/MidpointRuleMod_gr_88.gif]

[Graphics:../Images/MidpointRuleMod_gr_89.gif]
[Graphics:../Images/MidpointRuleMod_gr_90.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004