To find: The interval for the
To identify: The property of the integral used to obtain the solution.
Answer to Problem 50E
The value of the integral function lies between
The “comparison property 8 of integral” is used to calculate the value of integral.
Explanation of Solution
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
Chapter 5 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
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