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

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Chapter 5.4, Problem 5E
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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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Evaluating a Definite integral using a Geometric Formula In Exercises 1–6, sketch the region whose area is represented by the definite integral. Then use a geometric formula to evaluate the integral. See Example 1.

∫ − 3 3 9 − x 2   d x

To determine

To graph: The definite integral ∫−339−x2dx and calculate its area using geometric formula.

Explanation

Given Information:

The provided integral is,

∫−339−x2dx

Graph:

Consider the integral,

∫−339−x2dx

The function is f(x)=9−x2.

For x=−2,

Substitute x=−2 in the f(x)=9−x2 as below,

f(−2)=9−(−2)2=9−4=5=2.36068

For x=−1,

Substitute x=−1 in the f(x)=9−x2 as below,

f(−1)=9−(−1)2=9−1=8=2.828

For x=0,

Substitute x=0 in the f(x)=9−x2 as below,

f(0)=9−(0)2=9=±3

For x=1,

Substitute x=1 in the f(x)=9−x2 as below,

f(1)=9−(1)2=9−1=8=2

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