Exercises for Section 8.5.  Indented Contour Integrals

      Instructions for Exercises 1-15.  Use residues and an indented contour to compute the integral.

Exercise 1.   .
Solution 1.

Exercise 2.   .
Solution 2.

Exercise 3.   .
Solution 3.

Exercise 4.   .
Solution 4.

Exercise 5.      and   .
Solution 5.

Exercise 6.      and   .  
Solution 6.

Exercise 7.      and   .  
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.     and   

Hint:  Use trigonometric identity .  
Solution 15.

Exercise 16.   .

Hint.  Use the contour    shown in the figure below,

and establish that  .
Solution 16.

Exercise 17.   .

Hint.  Use the contour    shown in the figure below,

and establish that  .
Solution 17.

                    The contour    for Exercises 16 and 17.

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