BuyFindarrow_forward

Study Guide for Stewart's Single V...

8th Edition
Stewart + 3 others
ISBN: 9781305279148

Solutions

Chapter
Section
BuyFindarrow_forward

Study Guide for Stewart's Single V...

8th Edition
Stewart + 3 others
ISBN: 9781305279148
Textbook Problem

True or False:

The Mean Value Theorem for Integrals is a restatement of the Mean Value Theorem (of Chapter 4) but stated in terms of a definite integral instead of in terms of a derivative.

To determine

Whether the statement “The Mean value Theorem for integrals is a restatement of the Mean value Theorem but stated in terms of a definite integral instead of in terms of a derivative.

Explanation

Definition used:

The mean value theorem for integrals is a direct consequence of the mean value theorem for derivatives.

Theorem used:

Mean Value Theorem for derivatives:

“Let f be a function that satisfies the following hypothesis:

1. f is continuous on the closed interval [a,b].

2. f is differentiable on the open interval (a,b).

Then, there is a number c in (a,b) such that f(c)=f(b)f(a)ba.

Or, equivalently, f(b)f(a)=f(c)(ba)”.

The mean value Theorem of integrals:

If f is continuous on a closed interval [a,b] there exists c[a,b] such that abf(x)dx=f(c)(ba), where abf(x)dx is the area under y=f(x) and f(c)(ba) is the area of the rectangle with width (ba) and the height f(c).

Proof:

The result of mean value theorem of derivatives is f(c)=f(b)f(a)ba by using the theorem mentioned above

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

Additional Math Solutions

Find more solutions based on key concepts

Show solutions add

The equation that best describes the curve at the right is:

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercises 21-24, find the distance between the given points. 22. (1, 0) and (4, 4)

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

Convert the expressions in Exercises 8596 radical form. 3.1x4/3117x1/7

Finite Mathematics and Applied Calculus (MindTap Course List)