From Physical to Arithmetic Integrals - Achieving Complete Agreement with Intuition

[@lucafurer9580]

I wish my teachers in my hometown, Des Moines, were as clear and concise as you are! Thank you! ❤😊

[@JBerry00]

I completely agree, could not have said it better

[@JBerry00]

Great video! Really helped my understanding! Thank you

[@MathTheBeautiful]

Thank you for letting me know!

[@thallesaraujo7814]

I have the feeling that this is how integrals should be taught in introductory courses and books even if out of the intention of moving towards differential geometry. Edit: I missed Lionel at 14:46.

[@MathTheBeautiful]

I hope it's one of the possible ways!

[@theoremus]

I also like the term invariant.

[@MathTheBeautiful]

Let's start a club!

[@theoremus]

@@MathTheBeautiful In the Algebraic Calculus, the invariant plays key role, not the limit. The limit is somewhat nebulous and ill defined (magic and mysterious) whereas the invariant is crisply defined. No wonder it took 200 years to define the limit (epsilon delta). Question, is Epsilon Delta definition of the limit the gold standard (bulletproof) definition? Personally, I struggle with understanding it.

[@zoerachfal3729]

👏👏👏

[@evankalis]

Would it be possible to make the parameter not monotone increasing? And if so what would that do to the integral?

[@MathTheBeautiful]

Yes. Some things will survive and some things will break!

[@Christopher-e7o]

X,2x+5=8

[@Pluralist]

[@Christopher-e7o]

+/-

[@MathTheBeautiful]

Best to avoid ± whenever possible, I say