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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.

g ( t ) = t 3 + t 2 ,     [ 1 , 3 ]

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 g on the interval [a, b].

2) Formula:

gave=1b-aabg(x)dx

3) Given:

gt=t3+t2,     [1, 3]

4) Calculation:

Here,

gt= t3+t2,   a=1 and b=3

Substituting all the above in the formula,

gave=13-113t3+t2dt

Simplify.

gave=1213t3+t2dt

Here, we need to use the substitution method.

Let

u=3+t2 thus, du=2tdttdt=du2

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

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