Question: If av() really is a typical value of the integrable function (x) on [a, b], then the constant function av() should have the same integral

If av(ƒ) really is a typical value of the integrable function ƒ(x) on [a, b], then the constant function av(ƒ) should have the same integral over [a, b] as ƒ. Does it? That is, does pb ["av(1) dx = f* f(x) a f(x) dx?

Give reasons for your answer.

pb ["av(1) dx = f* f(x) a f(x) dx?

Step by Step Solution

★★★★★

3.42 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

ANSWER Yes the constant function avf has the same integral over a b a... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Planning is one of the most important management functions in any business. A front office managers first step in planning should involve determine the departments goals. Planning also includes...

KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...

The head-nurse in a hospital would like to have a profile of the patients that come to her ward. a. What would be the nature of the study that would be designed - Exploratory, descriptive, or...

Feedback: #1: This is not the argument in this reading passage. (0/4). Question 1: Summarize the Riemann sum argument that gives the formula of area as a double integral. Hint 1: Read the subsection...

Question 1: Summarize the Riemann sum argument that gives the formula of area as a double integral. When computing these, you might have memories of Calculus I and finding the area of regions. This...

3. Solve the initial value problem 12, y'(0) = 2, y(0) = 0 4. If the differentiable functions F(x) and G(x) both solve the initial value problem dy = f(x), y(To) = 90 on some interval I, must F(x) =...

10 Green's functions for PDEs In this final chapter we will apply the idea of Green's functions to PDEs, enabling us to solve the wave equation, diffusion equation and Laplace equation in unbounded...

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Section 6.5 Reading Assignment: Work and Fluid Forces Answer Only Exercise 1, 2, and 3 by using a screenshot provided Calculus Pearson textbook. Make sure you read these three questions very...

3. a. Management of one 3 PL company decided to invest an amount of 10 lakhs for equipment. Due to the automation, there is an effort-saving of 1 minute/order. Assume there is a constant order of...

Explain the combined effects of these events on Canadian real GDP and the price level, starting from a position of long-run equilibrium. The following events have occurred in the history of Canada: ...

Ribidpro incorporated had mone than $ 1 , 0 0 0 . 0 0 0 of tasable income two years prior to the current yeat it would like to use its prion - year tax liability ( which was very low but above zero )...

EXERCISE 3.6. Consider a binary mixture of particles of types 1 and 2, whose Gibbs free energy is given by where n = n + n, n and n are the mole numbers, and x and x2 are the mole fractions of...

Find an equation for each ellipse. Graph the equation. Foci at (2, 0); length of the major axis is 6.

Find an equation for each ellipse. Graph the equation. Foci at (0, 2,); length of the major axis is 8.

Find an equation for each ellipse. Graph the equation. Focus at (-4, 0); vertices at(5, 0)

At January 1, 2025, Sunland Company's outstanding shares included the following. 298,000 shares of $50 par value, 7% cumulative preferred stock 921,000 shares of $1 par value common stock Net income...

Calculate the Variance of the Rate of Return, Var(R)

chapter 12 TIoMEWOTR PA12-2 Computing Cash Flows from Operating Activ The income statement and selected balance sheet information for Direct Pro ended December 31 are presented below. Income...