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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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Chapter 5.5, Problem 7E
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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Finding the Area Bounded by Two Graphs In Exercises 1-8, find the area of the region. See Examples 1, 2, 3, and 4.

f ( x ) = 3 ( x 3 − 1 ) g ( x ) = 0

Chapter 5.5, Problem 7E, Finding the Area Bounded by Two Graphs In Exercises 1-8, find the area of the region. See Examples

To determine

To calculate: The area bounded by the function f(x)=3(x3−x) and g(x)=0.

Explanation

Given Information:

The provided function is f(x)=3(x3−x) and g(x)=0 and the provided graph is shown below,

Formula used:

The function f(x) and g(x) are the continuous function on interval [a,b] and g(x)≤f(x) for all x in [a,b], then, the area bounded by the graphs of f(x) and g(x),x=a and x=b is,

A=∫ab[f(x)−g(x)]dx

Calculation:

Consider the provided function is f(x)=3(x3−x) and g(x)=0.

In the provided function f(x)=3(x3−x) and g(x)=0 where, f(x)≤g(x).

Now, from the provided graph, the limit of the function is x=−1 and x=1.

In the provided graph g(x)≥f(x)

Now, the area bounded the curve f(x)=3(x3−x) and g(x)=0 from point x=−1 and x=1

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