Explaining why Integrating gives the area under a curve?

[@oofsper]

Well done, kudos to all such math youtubers. However, what you presented to us was a mathematical proof that Integration gives the area of a function but what I assumed from the title was that you were going to give a practical and actual proof that why does following random steps of integration gives you the area of the curve and that is why I got a lil bit clickbait-ed. What I actually mean is why differentiation is inverse of integration.

[@octs609]

very nice proof. Made it extremely easy for me to understand intuitively.

[@Learning_Sun]

Concise and a very neat explanation! Thank you!

[@edcoad4930]

I think about it in terms of the antiderivative rather than area under the curve. The function being differentiated is the gradient function of the anti-derivaritive. The bounds are merely the values of the antiderivative. No "area" to think about.

[@Ghaith7702]

Integration is a concept that still amazes me its not easy to visualize like the derivitive i wonder how Newton and Leibniz approached it

[@ssstudent123]

interesting but missing some step//proof on why lim is equal to derivative of A(x)

[@trompette4485]

Because that's the definition of a derivative. There is no proof, the derivative is what that limit is called.

[@thundercraft0496]

that's the definition of derivative

[@JoseTorresMates]

This is called the Fundamental Theorem of Calculus, for a good reason 😅

[@Sir_Isaac_Newton_]

It's so infuriating that this is the first time I've seen this simple proof of a counterintuitive theorem.