A solution to the backward problem would also have much larger implications, for the following reason: An area is, from an Archimedean standpoint, an infinite sum of infinitesimal rectangular strips. As such, an area is an integral. It’s the integrated collection of all the pieces put back together, an accumulation of infinitesimal change. And just as derivatives are more important than slopes, integrals are more important than areas. Areas are crucial to geometry; integrals are crucial to everything, as we’ll see in the chapters ahead.
