ELi5: If the “rate of change” of a function is a tangible way to understand derivatives, what is a similar way to understand integrals?

Question

I know it’s the “area under the curve”, but what does that mean exactly? Is there a physical or tangible way to explain it?

I understand that a derivative is rate of change at a specific point, and something like acceleration is rate of change of speed. But how can I visualize that speed is the “integral” of acceleration? What does that mean, and how does it relate to the area underneath?

In: 172

Answer 1

I always found using location the easiest.

The derivative of location (change in location over time) is velocity.

The derivative of velocity (change in velocity over time) is acceleration.

Integration is just going back the other way.

The sum of acceleration over time gives you the velocity at a given time.

The sum of velocity over time gives you the location at a given time.