   Chapter 5.4, Problem 6E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### 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. ∫ − 4 4 16 − x 2 d x

To determine

To graph: The definite integral 4416x2dx and calculate its area using geometric formula.

Explanation

Given Information:

The provided integral is,

4416x2dx

Graph:

Consider the integral,

4416x2dx

The function is f(x)=16x2.

For x=2,

Substitute x=2 in the f(x)=16x2 as below,

f(2)=16(2)2=164=12=3.4641

For x=1,

Substitute x=1 in the f(x)=16x2 as below,

f(1)=16(1)2=91=15=3.8729

For x=0,

Substitute x=0 in the f(x)=16x2 as below,

f(0)=16(0)2=16=±4

For x=1,

Substitute x=1 in the f(x)=16x2 as below,

f(1)=16(1)2=161=15=3

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