Module 16 :  Line Integrals, Conservative fields Green's Theorem and applications
Lecture 47 :  Conservative Vector Fields [Section 47.2]
47.2.4 Theorem (Existence of potential):
  Proof
 

Selecting , we have


If we write

then is differentiable at , with . Hence,

Thus, is differentiable with respect to and

Similarly, by choosing and , we will get

Theorems 47.2.1 and 47.2.4 give us the following:

 
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