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## Homework Statement

Prove that the vector field F = (2xyz + 1, x^2 z, x^2 y) is irrotational. Find the potential φ associated with F (i.e. find the function φ for which ∇φ = F).

## Homework Equations

## The Attempt at a Solution

I figure for the first part I just calculate the curl, but for the second part, does this mean potential energy? perhaps it is irrelevant to me working out this question but if potential energy is mgx then taking the derivative with respect to x would leave us with a force mg. I am not sure how I would approach the second part. Thanks