Example  6.9.  Show that  ,   
where   is the line segment from  ,  and is the portion of the parabola    joining  ,  as indicated in Figure 6.8.  

Figure 6.8  The two contours and joining  .

Explore Solution 6.9 (a)

(a)  Use the straight line segment connecting the points  ,  set up the parameterization and compute the contour integral.  Enter the function  .  

Method (i).  The integral can be computed using the real and imaginary parts.

Method (ii).  The integral can be computed using a complex integrand.

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