   Chapter 5.5, Problem 9E

Chapter
Section
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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