Example 8.  Find the analytic value of the integral  [Graphics:Images/MidpointRuleMod_gr_148.gif]  (i.e. find the "true value").  

Solution 8.

[Graphics:../Images/MidpointRuleMod_gr_149.gif]
[Graphics:../Images/MidpointRuleMod_gr_150.gif]


[Graphics:../Images/MidpointRuleMod_gr_151.gif]
[Graphics:../Images/MidpointRuleMod_gr_152.gif]

[Graphics:../Images/MidpointRuleMod_gr_153.gif]
[Graphics:../Images/MidpointRuleMod_gr_154.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004