Problem

Find the numbers $ b $ such that the average valu…

01:06

Problem 13 Easy Difficulty

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] $.

Answer

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

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 5

Average Value of a Function

Discussion

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Watch More Solved Questions in Chapter 6

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Video Transcript

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.

Amrita B.

Topics

Applications of Integration

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 6

Applications of Integration

Section 5

Average Value of a Function

Top Calculus 2 / BC Educators

Grace H.

Numerade Educator

Caleb E.

Baylor University

Michael J.

Idaho State University

Joseph L.

Boston College