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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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BuyFindarrow_forward

Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Find the average value of the function on the given interval.

f ( x ) = x 2 / ( x 3 + 3 ) 2 ,     [ 1 , 1 ]

To determine

To find:

The average value of the given function 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=x2x3+32,     [-1, 1]

4) Calculation:

Here

fx=x2x3+32,  a=-1 and b=1

Substituting all the above in the formula,

fave=11-(-1)-11x2x3+32dx

Simplify.

fave=12-11x2x3+32dx

Here, we need to use the substitution method.

Let

u=x3+3.  Then du=3x2dx,  so x2dx=du3

Since this is the definite integral, the limits of the integration also changes

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