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.
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.
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.
Concise and a very neat explanation! Thank you!
Integration is a concept that still amazes me its not easy to visualize like the derivitive
i wonder how Newton and Leibniz approached it
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.
interesting but missing some step//proof on why lim is equal to derivative of A(x)
Because that's the definition of a derivative. There is no proof, the derivative is what that limit is called.
that's the definition of derivative
This is called the Fundamental Theorem of Calculus, for a good reason 😅
It's so infuriating that this is the first time I've seen this simple proof of a counterintuitive theorem.