How come the inverse of a derivative is an integral?

Question

I can’t conceptually grasp this the same why I can grasp addition/subtraction (the opposite of adding stuff is to take it away), but if the derivative of a function is the slope at any given point, then why would the area under the curve be the opposite of that?

In: 2

Answer 1

You get the slope by dividing the change in the function by a very tiny “width” of input.

You get an integral by multiplying the continuously changing value of the function by a very tiny “width” of input.

Both operations are either multiplying or dividing the function by an infinitesimally small “width” of input and hence are inverses to each other, like how you multiply by 5 to reverse dividing by 5.