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

An example:
If you can integrate a formula of a flow rate, you get the total volume.

Real world most integration is done already and you won’t need it. because you deal with data points and rarely theoretical functions. Had to learn so much integration as an engineer but never had to do any in my industry.