Improper Integrals

Definition of Improper Integrals

If f(x) is continuous on (a,b] and not continuous at x = a, then we define




Example:

       


 

Improper Integrals Involving Infinity

We define





Example:

       


Exercises:  

  1.    

  2.    

  3.    

  4. Determine for which values of p the integral

     

  5.  Use the formula for arc length to show that the circumference of the semi-circle 

           

    is 

            pr


Vertical Asymptotes


          Definition

Let f(x) have a vertical asymptote at x = c.  Then





Example

Evaluate

       


Solution

       

 



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