Exercise 1.  ,  where C is the line segment from  .   

Solution 1.

See text and/or instructor's solution manual.

Answer.  .

Solution.  The function    is analytic on the entire complex plane, which is simply connected,

and    has    as an antiderivative.

Thus,  we can use Theorem 6.9 to obtain  

                                  
                              

                    The path of integration is the line segment from  .  

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell