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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

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

f ( t ) = t 2 ( 1 + t 3 ) 4 ,     [ 0 , 2 ]

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:

ft=t21+t34,     [0, 2]

4) Calculation:

Here, ft=t21+t34,  a=0 and b=2,

fave=12-002t21+t34dt

Simplify.

fave=1202t21+t34dt

Here, we need to use the substitution method.

Let u=1+t3, then  du=3t2dt,  so t2dt=du3

Since this is a definite integral, the limits of the integration also change

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