Example 6.10.  (a)   Show that      but that   ,  

where is the semicircular path from , in the upper half plane, and is the polygonal path from , respectively, shown in Figure 6.9.  

Figure 6.9  The two contours and joining  .  

Explore Solution 6.10 (a)

(a)  Use the semicircular path from -1 to 1 in the upper half plane,  set up the parameterization and compute the contour integral.  Enter the function  .  

Method.  The integral can be computed using a complex integrand.

(c) 2006 John H. Mathews, Russell W. Howell