The upshot is that dA = y dx = f(x) dx. Boom—that’s the fundamental theorem of calculus. Or, as it is more politely phrased nowadays (in our misguided era when differentials have been forsaken for derivatives), dA⁄dx = y = f(x). This is exactly what we found in chapter 7 with the paint-roller argument. One last thing: When we regard the area
