Solution 8 (a).

See text and/or instructor's solution manual.

Answer.  .

Solution.  The integrand    is analytic inside  ,  which is a simply connected domain that contains the circle  .

For this situation we can apply Theorem 6.4, the Cauchy-Goursat theorem (see Section 6.3) and conclude that the answer is zero,

                    .

                    The function    is analytic inside  .  

This solution is complements of the authors.

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