How to Determine the Potential of a Conservative, Central-Symmetric Force?

[Uku]

Homework Statement

Find the potential of the following conservative and central-symmetric force

\vec{F(\vec{r})}=\vec{r}f(\vec{r})

Homework Equations

\vec{F}=-\nabla U

The Attempt at a Solution

I can integrate by components?

F_{x}=-\frac{\partial U}{\partial x}

Getting: U_{x}=-\int xf(x)dx

Not sure on this..

 

[dextercioby]

It's a system of PDE's for the same function U_x doesn't exist, since U is a scalar. You should haveU = - \int x f(x,y,z) dx + g(y,z)