Integration and the fundamental theorem of calculus | Chapter 8, Essence of calculus

I'm afraid this integral discussion just isn't as "pleasing" as your derivative discussion.

One thing that annoys the heck out of me (not unique to you - it's everywhere) is the way integration is introduced in the most limited way possible. When I realized - LONG after my formal education was complete - that "the endpoints of an integration interval," "the boundary around a surface of integration," "the surface around a volume of integration," and so on were all EXACTLY THE SAME THING, and that a common "region / boundary" paradigm fit all of those - INCLUDING ORDINARY INTEGRATION - I almost fell over. THIS SHOULD BE INTRODUCED RIGHT AT THE START. That doesn't mean you immediately TEACH surface and volume integrals - that can come later. But the fact that even what you're about to do right now is just step one of a ladder of things that continues on up into higher dimensions is golden knowledge.

It's like the first stages of math (and science, for that matter) training are "dumbed down" as much as humanly possible, and I don't understand why.

17:08 im really struggling to unnderstad this parl

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The only thing that I can say after watching this video is "AURA".❤❤❤🎉🎉😊

@ 18:00 Did that car travel a tiny distance backwards, or did it rotate a tiny angle through aNoThEr DiMeNsIoN!? 🤣

Love you videos, they've helped and are helping A LOT!♥

Consider this a distanc-time graph. We dont know the distance function s(t), but we know the velocity function v(t).

At x=8 in the distance-time graph, d(distance function)/dt=the rate of change of distance, aka the velocity, i.e. v(8)

So, now if we reverse-engineer the derivative, we get s(t), which at time =8, is the total distance travelled.

This is also the AUC of the velocity-time graph (minus the s(t) at the start, of course, just in case they started driving not at 0).

commenting here so that I can come back to it later if I forget.

I watched this 4 years ago when taking calc 1 and barely understood it. Passed with a C by pure memorization. Taking calc II 4 years later (now) and bothered to stumble by here again and it makes perfect sense

The Fundamental Theorem of Calculus IS The Mean Value Theorem. The New Calculus YT channel has videos about the MVT/FTOC that actually explain why Calculus works for anyone who want to understand it, not this hand-waving 'approach'! Please, give it a shot regardless of any preconceived notions you may have.

i suppose you could say
Σ is used for the sum of a function incrementing an /integer/
∫ is used for the sum of a function of ε small /decimals/

thank you

9 year old video. 2.9 million views. 1 42 year old guy who's never really "got it" suddenly actually getting it. Thank you so much for these videos.

8:32 INTERROBANG SPOTTED !!!