Exercise 15.  Show that  [Graphics:Images/FunTheoremCalculusModHome_gr_209.gif],  where C is the line segment from  [Graphics:Images/FunTheoremCalculusModHome_gr_210.gif],  by parametrizing C.  

Solution 15.

See text and/or instructor's solution manual.

Solution.  Parametrize C with  [Graphics:../Images/FunTheoremCalculusModHome_gr_211.gif],  for  [Graphics:../Images/FunTheoremCalculusModHome_gr_212.gif].  Observe that    [Graphics:../Images/FunTheoremCalculusModHome_gr_213.gif].  

Then we see that    

                    [Graphics:../Images/FunTheoremCalculusModHome_gr_214.gif]



































 

This solution is complements of the authors.



































 

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