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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 5.2, Problem 50E

To determine

**To find:** The interval for the integral function *m*) and maximum value (*M*).

**To identify:** The property of the integral used to obtain the solution.

Expert Solution

The value of the integral function lies between

The “comparison property 8 of integral” is used to calculate the value of integral.

**Given information:**

The integral function is

**Show comparison property 8 of integrals:**

If

**Calculate:**

Consider the function **.**

The function

The integral function has absolute maximum value as *M* and absolute minimum value as *m.*

Modify the function

Compare Equation (2) with Equation (1).

The value of the function lies between its absolute maximum and absolute minimum value within limits

Thus, the property of integral “comparison property 8” is satisfied.

Therefore, evaluate the integral

The expression to find the value of the integral by using Property 8 of integral as shown below:

Substitute 0 for

**Conclusion:**

Compare Equation (2) with Equation (1).

The value of the function lies between its absolute maximum and absolute minimum value within limits

Thus, the condition to apply comparison property 8 of integral is satisfied.

Therefore, the “comparison Property 8 of integral” is used to evaluate function