Calculating average value of function over interval | AP Calculus AB | Khan Academy

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Here we find the average value of x^2+1 on the interval between 0 and 3.
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[@futsurepolaris6304]

The people who make these and put them online are angels.

[@brysontownsend6305]

So just take the integral and divide by the length of the integral. Cake.

[@eamonnsiocain6454]

You hope I find this interesting?
This is marvelous!
I teach Maths. This presentation is concise and exact. I'm showing it to my students when we reconvene after the Spring Break.

[@anonymoustraveller2254]

area under y=average value is equal to area under curve so we find area under curve by integration then we put it into the equation ,as simole as that.

[@zaarashaikh4833]

Bestt teacher❤❤❤

[@keerthic6925]

Using this technique can I find average of a step function With large interval?

[@emilc1826]

Like ur way of explaining :D

[@canadianiam]

thanks for the education

[@KaylahH]

This saved my life thank you!

[@ahmadelsayed009]

Thank you !

[@quriositysquared1028]

Really helpful

[@adalaza]

Blew this on one of my exams. Thanks for reminding me how to do it.

[@miyamotomusashi4556]

Thank you.

[@nicholaswakula1395]

helped lots thanks!

[@danachakra9912]

This is really helpful thank you!

[@kevinli9565]

amazing!

[@sezonisvafli]

this helped a lot, thanks :)

[@neerjakoul642]

Sum of all real numbers between 1 and 2 can be evaluated by just calculating the area under the curve of graph of y = x between 1 and 2. Is that really right???

[@fromessa6636]

You’re my digital day assignment bruh

[@watchmadisplay]

You missed the constant C

[@Triplechoco52]

Drumman Martínez But when evaluating the integral by Fundamental Theorom of Calculus Part 2, the C's will cancel out anyway. Try it out, find the antiderivative F(x) for the function f(x)=x²+1 and evaluate F(b)-F(a) with any random a, b value.

[@ethansu201]

Where does the 1 cone from? Is it area? How does he know? Help plz

[@ethansu201]

At 2:54

[@whydouneedtoknow2867]

I know this is really late but in case anyone is confused it's because you divide by 3, which is the same as multiplying by 1/3.

[@lauragayre8661]

Yes exactly! This is so late too lol but he’s basically saying that since an integral finds the area under a curve, and since area is width*height (in simple terms), we can divide the area by the width to find the average height.

[@ysiadmarie5778]

Average velocity and average value is the same thing ?

[@iloveramennoodle01]

Is one always above the b-a, in the beginning of the equation?

[@amandadoyle2118]

Yes, if you are using the average value theorem.

[@sheerinsubekti9007]

gosh

[@Neha-jg6zx]

i just... you are amazing

[@aysenilhasdemir7741]

Everybody know formula.

[@aftabansari3845]

how to find that c value

[@themysticcuber992]

You don't need to use the c value in this case. This is because, based on the Fundamental Theorem of Calculus, (F(b)-F(a), you will have two integrals that have c in them, and when you subtract them, they cancel out, so you don't need to find a c when doing average value and finding definite integrals.

[@subbaraomaguluri2529]

How 1/3 came

[@YOUSIF3]

b-a=3-0=3

[@MastaChief10]

ah so you divide by the end point thought so :(

[@yaluman.]

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[@TrenMonster]

TF is an anti derivative LMFAO I'm screwed tomorrow

[@dwade22100]

WHAT

[@uhohspaghettio9940]

lauren ferry is really hot!!!!!!!!!

[@Orexll]

Forst!