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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 ) = 3 x + 2 ; [ 1 ,   5 ]

To determine

To calculate: The average value of a function f(x)=3x+2 over the interval [1,5] 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)=3x+2.

Formula used:

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

Average value=1baabf(x)dx

Calculation:

Consider the function,

f(x)=3x+2

Now, apply the formula of average value of the function f(x)=6x over the interval [0,3] as,

Average value=151153x+2dx=14[3ln|x+2|]15=34[ln7ln3]=34ln(73)

So the average value is 0

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