Exercises for Section 8.2.  Trigonometric Integrals

Instructions for Exercises 1-16.  Use residues to find the value of the integral.  

Hint.  The following substitutions will be useful.  

                    

Exercise 1.  .  
Solution 1.

Exercise 2.  .  
Solution 2.

Exercise 3.  .  
Solution 3.

Exercise 4.  .  
Solution 4.

Exercise 5.  .  
Solution 5.

Exercise 6.  .  
Solution 6.

Exercise 7.  .  
Solution 7.

Exercise 8.  .   
Solution 8.

Exercise 9.  .  
Solution 9.

Exercise 10.  .  
Solution 10.

Exercise 11.  .  
Solution 11.

Exercise 12.  .  
Solution 12.

Exercise 13.  .  
Solution 13.

Exercise 14.  .  
Solution 14.

Exercise 15.  ,   where   are real  and  .  
Solution 15.

Exercise 16.  ,  where   are real  and  .  
Solution 16.

(c) 2008 John H. Mathews, Russell W. Howell