Example 8.13.  ,  

but Equation (8-7) tells us that the improper integral of    over   doesn't exist, because the calculation  

                is undefined .  

Therefore we can use Equation (8-8) to extend the notion of the value of an improper integral, as Definition 8.2 indicates.  

Explore Solution 8.13.

Enter the function    and investigate the Cauchy Principal Value .

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