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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.4, Problem 60E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Average Value of a Function In Exercises 53-60, find the average value of the function on the interval. Then find all x-values in the interval for which the function is equal to its average value.

f ( x ) = 1 ( x − 3 ) 2 ; [ 0 , 2 ]

To determine

To calculate: The average value of a function f(x)=1(x−3)2 over the interval [0,2] and evaluate all values of x at which the function is equal to its average value.

Explanation

Given Information:

The average value of a function is f(x)=1(x−3)2.

Formula used:

The average value of the function f in a closed interval [a,b] is defined as,

Average value=1b−a∫abf(x)dx

Calculation:

Consider the function,

f(x)=1(x−3)2

Now, apply the formula of average value of the function f(x)=6x over the interval [0,2] as,

Average value=12−0∫021(x−3)2dx=12∫02(x−3)−2dx=[−12(x−3)]02=12−16

So, the average value is, 13

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