Find the potential energy function

[Calpalned]

Homework Statement

A particle is constrained to move in one dimension along the x-axis and is acted upon by a force given by ##\vec F (x) = \frac{-k}{x^3} \vec i ## where ##k ## is a constant with units appropriate to the SI system. Find the potential energy function ##U(x)##, if U is arbitrarily defined to be zero at x = 2.0 m, so that ##U(2.0 m) = 0 ##

Homework Equations

## \Delta U = -W = \int \vec F * dl ##

The Attempt at a Solution

The textbook says that answer is ##U(x) = \frac {k}{8} - \frac{k}{2x^2} ## but I got ##U(x) = \frac{k}{2x^2} - \frac {k}{8} ## Am I still correct?

 

[Cake]

Well, you're not far off, except the equation for Potential in the relevant equations is the negative integral of the force. Not just the integral. There's your issue.