The Mean Value Theorem For Integrals: Average Value of a Function

We are just about done with calculus! Before we go, let's talk about one more topic that brings together differentiation and integration. It's called the mean value theorem. There is one version that utilizes differentiation, and another version that uses integrals. Let's learn both, and see how they can both be used to compute the average value of a function over some interval.

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[dreamchaser]

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[raihansk]

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[imbatman]

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[williamwashington]

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[jules]

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[thedaranesianconfederation]

Hey professor dave,
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Have you consudered doing a few episodes on differential equations?

[agumondigimon]

Thank you this video was really helpful!

[abriellh]

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[amitnayak]

Sir, we want a video on Average value of logarithmic function.

[Ando]

if calculate f(b)-f(a)/b-a it will results 1, while with integral we got 2, why ??? 5:20

[bmohan]

Can anyone explain the comprehension problem solving with mean value theorem with differentiation

[asheranuanai]

Thanks for the vedio.can you do for the function f(x)= x+1 on the interval (3, 8)

[servandum]

I get 4.5 on the last example since the integral of that function was not evaluated

[smashwagon]

lets find some averages? I'm right here man

[watching]

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