WORK DONE BY A VARIABLE FORCE
If a force remains constant over the distance through which it acts, then the work
done by the force is just the product of force and distance. However, if the force
doesn’t remain constant, then the work done by the force isn’t just a simple product.
Focusing only on displacements that are along a straight line (say the x-axis), let F
be a force whose component in the x direction varies with position according to the
equation F = F(x). If we have a graph of F versus x, then the work done by F as it
acts from x = x 1 to x = x 2 is equal to the area bounded by the graph of F, the x-axis,
and the vertical lines x = x 1 and x = x 2.