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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

(a) Find the average value of f on the given interval.

(b) Find c such that f a v e = f ( c ) .

(c) Sketch the graph of f and a rectangle whose area is the same as the area under the graph of f.

f ( x ) = ( x 3 ) 2 ,     [ 2 , 5 ]

To determine

(a)

To find:

The average value of f on the given interval.

Explanation

1) Concept:

Use the formula for the average value of f on the interval [a, b].

2) Formula:

fave=1b-aabf(x)dx

3) Given:

fx=x-32,     [2, 5]

4) Calculation:

Here fx=x-32, a=2 and  b=5

Substituting all the above in the formula,

fave=15-225x-32dx

Simplify.

fave=1325x-32dx

Integrating,

=1

To determine

(b)

To find:

The value of c such that fave=f(c)

To determine

(c)

To sketch:

The graph of f and rectangle whose area is same the area under the graph of f

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