Proof of the Fundamental Theorem of Calculus

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In this video I'm presenting a neat proof of the Fundamental Theorem of Calculus (the version with antiderivatives), and at the same time I'm giving a review of integration since it is fundamental to my proof of the FTC. Note that this proof is not necessarily better (mathematically) than the proof with epsilons and deltas, but it is definitely neater. Enjoy!

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What an enthusiasm and happiness to teach math.
I also enjoy with the same spirit. Thank you.

samarthsai

For everyone who already know the definition of an integral
12:11

isabelacanoacosta

Yes! I've waited for so long for this video. But now I'm really curious about how Dr πM will do the epsilon delta proof because it wasn't very clear when i learned it at college.
You're great Dr πM :D

rubentuquerrez

He looked so happy and passionate when doing maths and proving this XDD

tigerexo

This video is so cool. Such a clear proof of FTC. All my mathematical life I've been waiting for this. I never got the standard textbook proofs through my head. I always got bogged down in the epsilons and deltas.

Jack_Callcott_AU

Dr. (pi)M is the best! (Sorry, I don't have any pi symbol...)

unknownaccount

It's a bit sad that many pointless channels have millions of subscribers and this one has just 4.8 thousand yet. Great work!

srpenguinbr

I never understood why it's named after Riemann ?
I mean didn't Newton and Leibniz were the one who invented/discovered calculus ? So it's obvious that they would have thought of cutting the interval into n pieces and all that . (obviously)
So why it's named after Riemann ?

darkseid

Hey Dr. Peyam! This video is incredible! If you get a chance, can you do a proof for the other fundamental theorem of calculus? I would love that!

null

Sweet. So he used MVT to prove FTC2, but can MVT be proven independently or does it require FTC to prove it?

richardaversa

That was great, i was kinda frustrated with math today, but when you wrote down that mean velue theorem, everything just clicked and fealt great.

Domzies

Good job but You spent almost 10 minutes just to explain Riemann's sum for f'(x) on the interval [a, b] though you must have considered that most of who came to watch the proof are supposed to already know how to do that and whats the definition of the definite integral
Also I have a question; if the proof of the FTC implies that the function we are integrating is continuous then why are there integrable but not continuous functions?

someone

The more I watch Dr. Peyam (sorry, π-M!), the more I enjoy him.

benniepieters

so awesome!.... I never knew that about the definition of Reiman integral.

richardfredlund

What is the fear of epsilon and delta? They very easy to understand and actually it helps a lot to follow abstract limits later on!

hqs

Pi, M. Now I know how to pronounce your name.

蔺美云

Great video, but I'm not gunna lie, I've never seen anybody with a Ph.D. in Math draw a more pathetic looking capital-sigma as you did around 9:32 :-)

randyhelzerman

You are the best! Me and my mom love you! Saludos desde México!

TheMauror

Thanks a lot! I love your enthusiasm for maths

Julefikar

respected you discus this theorem for which path kindly explain the path also

wahidrehman

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