7 (g).  Evaluate  ,   where C is the upper half of  .  

Solution 7 (g).

See text and/or instructor's solution manual.

Answer.   .  

                    The contour      for   .

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

                      and  ,  
                    
                    then

                       

The last two real integrals are computed using

                      

                    and

                      

This solution is complements of the authors.

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