Example 6.1.  Show that  [Graphics:Images/ComplexIntegralMod_gr_7.gif].  

Explore Solution 6.1.

Method (i).  Expand the integrand f[t] into its real and imaginary parts, then integrate u[t] and v[t].

[Graphics:../Images/ComplexIntegralMod_gr_14.gif]





[Graphics:../Images/ComplexIntegralMod_gr_15.gif]

 

 

 

Method (ii).  Compute the integral directly using a complex function for the integrand.

[Graphics:../Images/ComplexIntegralMod_gr_16.gif]





[Graphics:../Images/ComplexIntegralMod_gr_17.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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