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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 71–76, 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 ) = x 2 + 2 ; [ 3 , 3 ]

To determine

To calculate: The average value of function f(x)=x2+2 on interval [3,3] and find all x-value in the interval for which the function f(x)=x2+2 is equal to its average value.

Explanation

Given Information:

The provided function is f(x)=x2+2 and interval is [3,3].

Formula used:

The average values of function f(x) over closed intervals [a,b] is given by,

Average values=1baabf(x)dx

The fundamental theorem of calculus:

abf(x)dx=F(b)F(a)

Here, F is function such that F(x)=f(x) for all x in [a,b].

Calculation:

Consider the function:

f(x)=x2+2

Now apply the average values formula for function f(x)=x2+2 over closed intervals [3,3],

Average values=13003(x2+2)dx

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