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

In case is to be conservative with potential , we should have

                                      --------(41)

 

                                               ----------(42)

and

                                     ----------(43)

A general function which satisfies can be obtained as follows. First we integrate with respect to . This gives us

             ----------(44)

where is a continuously-differentiable function of -variables. But then, differentiating with respect to and using , we have

.

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