>At no point did anyone think to explain that we were measuring the areas under curves, or their rates of change
In my experience you get taught the definition of a derivative of a function at a point is equal to the instantaneous rate of change and that integrals are defined as a Reimann Sum, the sum of the area under the curve. Everything in the class comes from building on top of those definitions.
In my experience you get taught the definition of a derivative of a function at a point is equal to the instantaneous rate of change and that integrals are defined as a Reimann Sum, the sum of the area under the curve. Everything in the class comes from building on top of those definitions.