Chapter 6.5, Problem 4PT

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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

1.

2.

Then, there is a number

Or, equivalently,

*The mean value Theorem of integrals:*

If *f* is continuous on a closed interval

**Proof:**

The result of mean value theorem of derivatives is

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