Extra Example 1.  [Graphics:Images/IntegralsRationalMod_gr_16.gif],  

and Equation (8-7) tells us that the improper integral of  [Graphics:Images/IntegralsRationalMod_gr_17.gif]  over [Graphics:Images/IntegralsRationalMod_gr_18.gif]  also diverges to [Graphics:Images/IntegralsRationalMod_gr_19.gif], because  

            [Graphics:Images/IntegralsRationalMod_gr_20.gif].  

[Graphics:Images/IntegralsRationalMod_gr_21.gif]

Explore Extra Solution 1.

Enter the function  [Graphics:../Images/IntegralsRationalMod_gr_22.gif]  and investigate the Cauchy Principal Value .

[Graphics:../Images/IntegralsRationalMod_gr_23.gif]

[Graphics:../Images/IntegralsRationalMod_gr_24.gif]

[Graphics:../Images/IntegralsRationalMod_gr_25.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell