What is Work along a path?

Let a force $\vect F$ act on a body moving along any path from $A$ to $B$: cut the path into displacements $\vect{\dd\ell}$ so short that each is straight and $\vect F$ barely changes along it. Each step earns the small work $\scal{F}{\dd\ell} = F\,\dd\ell\cos\theta$ (Chapter 17), and the work along the path is their sum, $W_{AB}(\vect F) = \sum \scal{F}{\dd\ell}$ — which on a straight path with constant force collapses to last year’s $F \times AB \times \cos\theta$.