Module 16 :  Line Integrals, Conservative fields Green's Theorem and applications
Lecture 47 :  Conservative Vector Fields [Section 47.2]
 

Practice Exercises

(1)
 Show that

is a conservative vector field by finding a function such that .

Answer
 
(2)
 Show that , for some , where
 


and hence compute , where is

  Answer
   
(3)
 Show that the line integral
 

is not independent of the path .

   
(4)
Show that the vector field
 


is not conservative by evaluating the integrals


where is the curve and is the curve

.

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