Example 3.  Find the analytic value of the integral  [Graphics:Images/BooleRuleMod_gr_88.gif]  (i.e. find the "true value").   

Solution 3.

The integral of  [Graphics:../Images/BooleRuleMod_gr_89.gif]  can be determined.

[Graphics:../Images/BooleRuleMod_gr_90.gif]
[Graphics:../Images/BooleRuleMod_gr_91.gif]

The value of the definite integral

[Graphics:../Images/BooleRuleMod_gr_92.gif]
[Graphics:../Images/BooleRuleMod_gr_93.gif]


[Graphics:../Images/BooleRuleMod_gr_94.gif]
[Graphics:../Images/BooleRuleMod_gr_95.gif]

[Graphics:../Images/BooleRuleMod_gr_96.gif]
[Graphics:../Images/BooleRuleMod_gr_97.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004