Solution 9.

See text and/or instructor's solution manual.

Answer  .  

                    The points    and    which lie on the contour  .

Solution Method I.   The function is    and the curve is     for    and we obtain

                       and  ,  
                     
then

                       

The last two real integrals are computed using

                      
                    
                    
                    and
                    

                      

We are done.   

Aside.  We can let Mathematica double check our work.

We are really done.  

Solution Method II.   We could also use the following complex computations.

The function is    and the curve is    for    and we obtain

                      and  ,  
then

                       

Here we have used the calculations indicated by equation (6-8) in Section 6.1:

                       

We are really really done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

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