Mean value theorem for integrals | AP Calculus AB | Khan Academy

Here Sal goes through the connection between the mean value theorem and integration.

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

[DandoBorusu]

Very Good! Chapter 4 test tomorrow. I like your new program and writing tool, its a lot easier to pay attention!

[sl]

But would that be considered circular logic as we implicitly used Foundamental Theorem of Calculus to proof Mean Value Theorem?

[justanearthling]

It's a very interesting way to see Lagrange Theorem, useful for a demostration and to connect a fuction to his primitive.

[meschmid]

Thank you for your video's. They very helpful

[tomglansholm]

I dont understand, you used the second part of the fundamental theorem of calculus to prove the mean value theorem, but you need the mean value theorem to prove ftoc part two... hmm ..

[watching]

What is this used for in applications (real life) is this to find average position or velocity between a time range?

[OmegaCraftable]

Wait, but when f'(c) = (1\b - a) ∫f(x)dx, how can this provide multiple solutions to account for the different values of x that can be c.

[raineestudy]

Khan I'm watching this to understand your proof on the Fundamental Theorem of Calculus which uses the Mean Value Theorem for Integrals as a lemma but then you use FTC at 4:50 in this video so the logic between your videos is circular. I can't understand :/

[abd-elrahmanmohamed]

Great ... I read it from Wikipediak , but it doesn't make sense . Here it's very clear .