Solution 20.

See text and/or instructor's solution manual.

Answer.  The value of the function    is a "weighted average" of values of     taken points   along the contour  C.  

                              .  

Up until now one might not have seen a function that is defined in terms of a contour integral.

Some common ways to define a function in calculus are:  with a formula,  with a table of values, with a limit.  

Often time a function is defined with an integral such as  .

Aside.  If we write     

then the function   is often times called the "kernel."

This solution is complements of the authors.

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