Is a Central Force Always Conservative?

[subwaybusker]

Homework Statement

Show that a central force between two objects, ie. one that acts along the vector connecting their centres, r[tex]^{$$\Downarrow$$}[/tex],with a strength that depends on only r, is a conservative force. I am supposed to do this in cartesian coordinates and show that the work is zero or that the work only depends on the endpoints.

Homework Equations

The Attempt at a Solution

I know that F=F(r)r, and that W = $$\int$$F. dr from A to A = 0. I tried breaking it into x,y,z components because of the cartesian hint, but I don't know what to do from there.

 

[subwaybusker]

nobody?