Work done by a constant force

When the force $F$ acting on a body stays constant in both magnitude and direction throughout the motion (though the angle $\theta$ between $F$ and the path can still be fixed by the geometry), the small work done for a small displacement $dr$ is

Because $F$ and $\theta$ do not change, this can be integrated directly over the whole displacement from an initial position $r_i$ to a final position $r_f$:

$W = \int_{r_i}^{r_f} (F\cos\theta)\,dr = (F\cos\theta)(r_f - r_i)$ …