Mean value theorem for integrals | AP Calculus AB | Khan Academy
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- Опубликовано: 12 сен 2024
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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.
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Very Good! Chapter 4 test tomorrow. I like your new program and writing tool, its a lot easier to pay attention!
From where r u?
So no examples
you can go to the khan academy website; you will find a lot of examples and also the answer and explanation of them.
This video save my life. Thank you.
Thank you very much
Thank you for your video's. They very helpful
But would that be considered circular logic as we implicitly used Foundamental Theorem of Calculus to proof Mean Value Theorem?
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 ..
I don't think these videos are set up to give a rigorous account of calculus, but rather just give you a vague idea of why the results in calculus seem plausible. With that said, another way to prove the mean value theorem for integrals is as follows:
Let m and M be the minimum and maximum values of f on [a,b], respectively. Then m≤f(x)≤M for all x in [a,b]. Integrating these inequalities and dividing by b-a, we obtain the inequalities m≤A(f)≤M, where A(f) denotes the average value of f over the interval [a,b]. We can now invoke the intermediate value theorem to conclude that there must be som point c in [a,b] such that f(c)=A(f).
Johannes nicely explained thanks
You dont need the fundamental theorem of calculus to prove the mean value theorem for integrals
You really need to work it out yourself bro...
What is this used for in applications (real life) is this to find average position or velocity between a time range?
It's a very interesting way to see Lagrange Theorem, useful for a demostration and to connect a fuction to his primitive.
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 :/
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.
MIND=BLOWN
Great ... I read it from Wikipediak , but it doesn't make sense . Here it's very clear .
4:08 the stars?
What happened at 6:00
IMO 2014 solutions please !!
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