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.