Essential University Physics: Volume 1 (4th Edition)

The work is equal to the integral of $F dx$. While we could compute these integrals, we instead can examine the area under each of the functions from 0 to 1. When doing so, we see that $x^2$ does the least work while $\sqrt{x}$ does the most work from 0 to one, for the latter function has the most area under its curve from zero to one while the former function has the least area under its curve from zero to one.