Fundamental theorem of calculus (Part 1) | AP Calculus AB | Khan Academy

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The fundamental theorem of calculus shows how, in some sense, integration is the opposite of differentiation. Created by Sal Khan.

AP Calculus AB on Khan Academy: Bill Scott uses Khan Academy to teach AP Calculus at Phillips Academy in Andover, Massachusetts, and heÕs part of the teaching team that helped develop Khan AcademyÕs AP lessons. Phillips Academy was one of the first schools to teach AP nearly 60 years ago.

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My debt to Khan Academy is one without end.

Heartofadracky

I like how he says, THE FUNDAMENTAL THEOREM OF CALCULUS

muzakkir

I learned more in 8 minutes and 2 seconds than a 50 minute lecture.

benderbendingrofriguez

Your computer hand-writing is amazing.

ender

I've returned to calculus later in life to refresh for an exam I'm taking. It's absolutely astonishing how I perceive this to be an overcomplication (not on Khans part, but mathematics overall). It almost seems like the fundamental theorem of calculus is constructed in such a way as to deter people from attempting to wrap their heads around it, even though it is an absolutely simple concept in itself. If you have an area under a curve on an interval [a, b] you can find the area under the curve from [a, x] so long as x < b. Like I said, absolutely mind boggling that such a thing is made out to be what is is. It's literally common sense.

blendertv

idek why people dislike this video! Khan Academy is really help (for me at least)!

rushipatel

EVERYONE! Watch this video at 1.25x regular speed! It's much faster and just as understandable! Good luck!

ozzlicious

I finished my calculus 1, 2 and 3 last semester. and yet I still enjoy watching these videos.
Also thank a lot sal, I got an A in all my calculus courses and in my ODE course.
and thanks a great deal to your clear intuitive explaination !

TheAhmedMAhmed

Sal "Let me write this down, this is a big deal." XD

M_Dragon

Thank you, you you guys are making this world a better world

andrewnorris

A nice video, the benefit of which was greatly augmented by my reading of the same topic in Wikipedia. Grateful thanks to all these philanthropic types!

deepakbellur

Thank You Khan Academy, this video was a HUGE help!

sajsanilkumar

Thank you for making math so much more interesting! :)

kennethwong

I watched this instead of going to my lecture
i'm a bad student

AimeeColeman

deadass would give my first born to this man if he asked. You js saved me from having my 8th mental breakdown this weeek thank yoy!

vanessaperez

The intuitive explanation is rather simple: the rate of change of the area under the curve, from x=a to x, evaluated at x, per small change of x, is in fact the height of the rectangle f(x) delX, i.e value of f(x) itself, at x.

milansekularac

wonderful...I hadn't understand a single word of my instructor, but now it is clear to me what the fundamental theorem is...THANKS KHAN ACADEMY....

quantaali

Wow. It finally clicked. Wow. Im on cal 2 and it finally clicked. TY so much! Now off to make this intuitive! :\

ebscoHOSTpub

I wished I had this available to me when I was learning calculus, college students are so fortunate to have resources like this. There is no excuse for failing calculus these days, and BTW I passed all my calc classes but I had to work really hard at it.

mrkattm

Lol, it's true, Sal is actually really good at writing with that mouse, something most of us absolutely cannot do

Papaconstantopoulos

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