Check out this dialogue between two calculus students (based on a true story):
- Devyn
- Ah. So now we have a connection between derivatives and integrals.
- Riley
- Right, the derivative of the accumulation function is the “inside” function.
- Devyn
- So how do we use this to compute area?
Sometimes it helps to think about the most basic examples. Consider
We know (by geometry) that this computes the area of a rectangle which equals . On the other hand, if we consider the accumulation function
we see that