Now we use the computer algebra system to calculate values of line integrals similar to the ones you approximated in Part 2. In this part we will concentrate on the functions f1(z) = 1/z and f4(z) = ez.
In Step 5 of Part 1 you calculated the line integrals of f1 and f4over the semicircles C4 and C5. Compare those calculations with the estimations obtained in Steps 4 and 5 of Part 2.
Now integrate both of the functions f1 and f4 over the whole unit circle centered at the origin traced out once counterclockwise from 1 back to 1.
Repeat Step 2 with the whole unit circle traced out once clockwise from 1 to 1. (Check to make sure the curve is traced out clockwise.)
How could the results of the calculations in Steps 2 and 3 have been determined in advance from the semicircle calculations recorded in Step 1?
