Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Question

Answered step-by-step

If $ f_{ave} [a, b] $ denotes the average value of $ f $ on the interval $ [a, b] $ and $ a < c < b $, show that$$ f_{ave} [a, b] = \frac{c - a}{b - a} f_{ave} [a, c] + \frac{b - c}{b - a} f_{ave} [c, b] $$

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Amrita Bhasin

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Calculus 2 / BC

Chapter 6

Applications of Integration

Section 5

Average Value of a Function

Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

Lectures

02:38

If $f_{\mathrm{ave}}[a, b]…

06:25

If $f_{\mathrm{vve}}[a, b]…

01:02

If $f_{\operatorname{mix}}…

03:40

Show that the average valu…

01:52

If $a< c< d< b,$ …

02:16

Suppose the average value …

01:32

01:43

Suppose that the average v…

04:46

Prove that if $f$ is conti…

we know the average value formula could be written with a beak, A, C and C B. Therefore, we know C minus a over B minus a times one over C minus A from a C. Kovacs detox is equivalent to one over B minus A from A to C of after box detox. And we know this can also be written as one over B minus a from sea to be after Rex detox. Given the fact that we are looking at the interval from A to B, we know we can write this as won over B minus A from A to B aftereffects. Detox is equivalent to the average value from A to B.

View More Answers From This Book

Find Another Textbook

04:20

A hospital blood bank conducts an annual blood drive to replenish its invent…

00:33

Solve the equation by factoring: X =9x+ 10 equation in factored form. Rewrit…

01:23

The vector (a,b,2) is perpendicular to the plane a?2x 3y + 1. What is th…

07:01

35. Pricing A concert promoter needs t0 make *42,0uu TJOU from the sale of 1…

03:16

QuestionWhich of the following is not an assumption of the multiple line…

05:31

35 Better DY this airline? a Getting Deals. To better understand their fina…

03:04

point) If P(A) = 0.5, P(B) = 0.5 and P(A and B) = 0.05, find the following p…

02:14

Problem 12. tennis club has 2n members_ We want to pair uP the mem- bers by …

02:48

For Problems 4, 5, and 6. solve the linear differential equations dy + 2y = …

Find the open intervals on which the function is increasing and decreasing_ …