Chapter 6.6, Problem 4ES

Suppose that a variable force $F\left(x\right)$ is applied in the positive $x\text{-}$ direction so that an object moves from $x=a$ to $x=b$ . Relate the work done by the force on the object and the average value of $F$ over $\left[a,b\right]$ , and illustrate this relationship graphically.