Example 6.20. Show
that
, where
C is the unit
circle
, taken
with positive orientation.
![]()
Figure 6.32 The simply connected domain D shown in Examples 6.19 and 6.20.
Explore Solution 6.20.
Enter the function
.
![[Graphics:../Images/FunTheoremCalculusMod_gr_70.gif]](../Images/FunTheoremCalculusMod_gr_70.gif)
![[Graphics:../Images/FunTheoremCalculusMod_gr_71.gif]](../Images/FunTheoremCalculusMod_gr_71.gif)
![[Graphics:../Images/FunTheoremCalculusMod_gr_72.gif]](../Images/FunTheoremCalculusMod_gr_72.gif)
Another approach is to parameterize the integrand.
![[Graphics:../Images/FunTheoremCalculusMod_gr_74.gif]](../Images/FunTheoremCalculusMod_gr_74.gif)