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1. The problem statement, all variables and given/known data

Find a potential function for the conservative vector field F = <x + y, x - z, z - y>

2. The attempt at a solution

OK, we know that

(1) f_{x}= x + y

(2) f_{y}= x - z og

(3) f_{z}= z - y

We can then integrate (1) with respect to x, and we get

(4) f = (1/2)x^{2}+ xy + C(y,z)

We then differentiate (4) wrt y and get:

(5) f_{y}= x + C'(y,z)

Comparing (2) and (5):

(6) C'(y,z) = -z

Integrate this wrt z:

(7) C(y,z) = -(1/2)z^{2}+ C(y)

We then have the following expression for the potential function so far:

(8) f = (1/2)x^{2}+ xy + -(1/2)z^{2}+ C(y)

Then I'm stuck. Is my method correct so far?

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# Homework Help: Potential function for conservative vector field

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