Mean value theorem for integrals (KristaKingMath)

Learn how to use the Mean Value Theorem for integrals to prove that the function assumes the same value as its average on a given interval.

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Hi, I’m Krista! I make math courses to keep you from banging your head against the wall. ;)

Math class was always so frustrating for me. I’d go to a class, spend hours on homework, and three days later have an “Ah-ha!” moment about how the problems worked that could have slashed my homework time in half. I’d think, “WHY didn’t my teacher just tell me this in the first place?!”

[c-wayne-u]

Hi. I am a early retiree (enterprise technology architect). but still love math and science. I spend a couple nights a week tutoring grand kids and their friends at various stages of algebra, geometry, calculus, and computer science. Just ran across your videos and was very impressed with what you have done. I have added you to my list of resources. ;-)

[ThePinoyMamba]

Very well done K!!!
Every time it gets easier!
Love your easy approach, very analytical and on the spot.
Thanks!

[kristakingmath]

Glad I can act as a refresher.

I always wonder how my education would have been different if I were growing up with this technology.

[ReadyToRek]

Thank you, Krista! I'm studying to be an astrophysicist and every time some formal calculus problem comes up I know I have your videos to remind me of concepts I've forgotten. I wish I had these videos when I was in Calc I and II. :P

[MsReeses]

really good video! how did you know if you were supposed to use the mean value theorem or the intermediate value theorem?

[_harsh]

Your amazing teaching skills keep it up...
Could plse tell me the name of software you had used in video .
Chalk effect is looking quite good.

[kingzeroman]

THANK you, this was the clearest explanation I found.

[jayoberlander]

I was taught that with the mean value theorem for integrals you are supposed to integrate the function to find the value, set that equal to the function at c multiplied by the average and then solve for c to get the values?

[kristakingmath]

Awesome, Wayne!! Thank you! I hope the videos will be a resource to you and to the grand kids! And congrats on the early retirement... I hope you're having a blast!! :D

[hg.]

Had some head scratching in this one, but will move on and if it (the Mean Value Theorem) comes up again I can go back earlier vids and brush up. That's one of the beauties-benefits of Krista's videos.

[eyrar]

Thank you! This was so helpful I now plan on watching all of your calc videos before the test... Which is tomorrow...

[GundamDestiny]

hi, I just want to ask if you have any videos that teaches you on how to look at the equation and how the graph looks like (sin x^2, x^3, ect). im taking calculus 2 and my professor don't allow any calculators at all

[ryuyusuke]

Thank you so much, I love you !  Today is my final at night. Thank you for reassuring me.

[c-wayne-u]

Great videos. These are all totally awesome... THANKS.

[aimz]

So is average value the same as the mean value? I'm a little confused?

[Goldname]

What does it mean by average value of the function.

[Cub]

I love you!! you saved my life today!! :)

[MsReeses]

what "average" are you referring to?

[kristakingmath]

hang in there! It just takes practice.

[chetanmeena]

please share lecture on mvt in multi variables