Proof of fundamental theorem of calculus | AP Calculus AB | Khan Academy

Показать описание

The first part of the fundamental theorem of calculus tells us that if we define _(_) to be the definite integral of function Ä from some constant _ to _, then _ is an antiderivative of Ä. In other words, _'(_)=Ä(_). See why this is so. 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.

For free. For everyone. Forever. #YouCanLearnAnything

Khan Academy

Рекомендации по теме

Комментарии

After watching this 20 times I finally understand!

rajbirvirdi

Great vid! Very logical, really breaking the barrier that gives us students the thoughts "How could anyone figure this out? Surely one has to be a genius..."
Now I feel like the inventor(s) of the integral proof are actually human and were I one of them at that time I might have figured it out!

Big thanks!

danielgonzalezisaiev

Every-time Sal says "just for fun"
Me: " sure, just for fun."

celesteacosta

So, Sal casually took the derivative of F(x) just for fun and ultimately produced a proof for the fundamental theorem of calculus? That's genius right there.

No_BS_policy

I remember watching this video back when I was in my second semester of college. I didn't understanding a thing. Now, being in my sixth semester and watching it again, everything just clicks. It's nice to see some growth for a change.
(Btw, beautiful proof and splendid explanation, props!)

andresyesidmorenovilla

i really want to cry😂 i finally understand this TvT
i have been searching for the proof for 2 days😂 (cuz i really cant accept that formula if i dont understand where it comes from )
thank u

hojiaqian

has this still not won an oscar yet????

tornmyhibula

Aight I'll just watch it 20 more times

CyanKash

I have taken two semesters of calculus and have used this theorem so many times its second nature to me. However I never knew why this theorem worked until just now. I had no idea how the heck an infinite sum could be connected so directly to a derivative, and I didn't imagine it would be so simple. Now I finally understand better where this comes from and I'm so happy about that. Thank you so much Sal!

RyanProvchy

if sal had a dollar for every intuition he gave us
he'd be bill gates

ultimatepirate

you are such a great person. i attend a community college, and out teachers are horrible. my teacher has a huge asian accent and on top of that my registration time for classes was really horrible. i always loved math, but this quarter the only calc B class left open for me was with this asian teacher at 8PM. im really sleepy, hungry, and can't understand a word the teacher is saying. thank you so much for the help khan.

liverpooler

This is the innermost reasoning of Calculus, it's celestially beautiful!

hubenbu

the best one so far. every video I've watched before had left me with lots of questions. but this video gave me Intuitive understanding and mathematical understanding at the same time. thanks a lot
and big ups

smerdis

Well both t and x are placeholders for numbers that lie on the interval [a, b]. What the theorem says is that F' and f always have the same value when you evaluate them at the same number. The main reason that t is used instead of x in the integral is because there x is used as a fixed point denoting the upper bound of the integral and we must integrate with respect to a variable. Just as easily we could have written F(t) = integral from a to t of f(x)dx.

vko

Proofs for the theorems may seem monotonous but they actually give great insights into the concept.

That's the beauty of math.

AbhinavRawal

i am an eight grader and yet understood everything thanks to the teaching methods thank you!

spade

Choice of words: "RESORT to Squeeze Theorem". That's sort of how I feel about using the Squeeze Theorem as well.

joelgerard

its amazing how your new videos are always synced with what im currently doing in class...

stefan_dobre

Thank you so much for what you do. You make a difference in many peoples' lives, and I appreciate it.

gaufill

amazing explanation, I tried understanding it from my teacher and FAILED, but here its so flowing.. thanks!!

shalev

Proof of fundamental theorem of calculus | AP Calculus AB | Khan Academy

Proof of fundamental theorem of calculus | AP Calculus AB | Khan Academy

3 Levels of Proving the Fundamental Theorem of Calculus | #SoME3

A Simple and Beautiful proof of The Fundamental Theorem of Algebra

Proof of The Fundamental Theorem of Arithmetic

Proof of the Fundamental Theorem of Calculus (the one with differentiation)

The Fundamental Theorem of Calculus - Proof

Fundamental Theorem of Calculus Part 1

Fundamental Theorem of Algebra - Numberphile

Prime Numbers and the Fundamental Four - Historical Breakthrough

Real Analysis 56 | Proof of the Fundamental Theorem of Calculus

Proof of the Fundamental Theorem of Calculus

1st Fundamental Theorem of Calculus PROOF | Calculus 1 | jensenmath.ca

Fundamental Theorem of Calculus - Proof of Part 1 of the Theorem

a quick proof of the Fundamental Theorem of Calculus

Number Theory | Fundamental Theorem of Arithmetic

The Fundamental Theorem of Line Integrals // Big Idea & Proof // Vector Calculus

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

Fundamental Theorem of Calculus - Intro and Proof of Part 2 of the Theorem

PROOF of 2nd Fundamental Theorem of Calculus | Calculus 1 | jensenmath.ca

Fundamental theorem of calculus, how it works (Animation)

The Fundamental Theorem of Calculus: Redefining Integration

Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example

Number Theory | Lemma 1 for Fundamental Theorem of Arithmetic

The Fundamental Theorem of Arithmetic