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If $ f $ is continuous and $ \displaystyle \int_{1}^3 f(x) dx = 8 $, show that $ f $ takes on the value 4 at least once on the interval $ [1, 3] $.

there exists a $c$ such that $f(c)=4$

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 5

Average Value of a Function

Campbell University

Oregon State University

Harvey Mudd College

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:03

Evaluate $\int_{3}^{8} f^{…

01:00

If $ f $ is continuous and…

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Suppose that $ f(1) = 2 $,…

00:34

If $f$ is continuous and $…

01:17

03:22

Suppose that $f(1)=2, f(4)…

02:01

Show that if $f$ is contin…

02:31

If $ f(1) = 12 $, $ f'…

02:29

Calculate $F(4)$ giventhat…

we know we're gonna be using the mean value theorem, which essentially means that because of his continuous there exists a numbers see between the bounds of 123 such that the average value won over B minus A from A to B of our function after vax d X equals F f c. So we know this means that half of sea is 1/2 times ate half of eight is four. Therefore, there does exist to see such the F of CS four.

Numerade Educator

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