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

Antiderivative for one. Area under the curve, I think, is the easiest, but if we take the value of the area under the curve, we get a function where if we look at the rate of change of that function, we get the original function back.

Rate of change of position is velocity

The integral of velocity with respect to time gives the position