   Chapter 4, Problem 53RE

Chapter
Section
Textbook Problem

Using the Mean Value Theorem for Integrals In Exercises 53 and 54, find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the given interval. f ( x ) = 3 x 2 ,             [ 1 ,   3 ]

To determine

To calculate: The value(s) of c for the integrals f(x)=3x2,[1,3] over the given intervalusing the Mean Value Theorem.

Explanation

Given:

f(x)=3x2,[1,3]

Formula used:

Mean value theorem: If any function is differentiable and continuous in a given interval [a,b] then,

f(c)=f(b)f(a)ba

Calculation:

We will use the mean value theorem for the integral there must exists some c[1,3] such that

13f(x)dx=f(c)(31)

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

1. If f(x)=x+2x and g(u)=u+2u, is it true that f = g?

Single Variable Calculus: Early Transcendentals, Volume I

Solve the equations in Exercises 126. (x21)2(x+2)3(x21)3(x+2)2=0

Finite Mathematics and Applied Calculus (MindTap Course List)

Describe mathematical modeling in your own words.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Given f(x)=5x23xandg(x)=x+1,find(a)(fg)(x)(b)g(g(x))(c)(f0g)(x)

Mathematical Applications for the Management, Life, and Social Sciences 