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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