Solution 11.

See text and/or instructor's solution manual.

Answer.  .  

Solution.  On the contour    we have    so that  .

In the last integral, the integrand    is analytic everywhere.

Hence, by the Cauchy-Goursat Theorem we have   .  

Therefore,  .  

Solution using parameterization.  The function is    and the curve is    for  .   Then we obtain

                       and   ,  
then

                       

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

                        

We are 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