   Chapter 5, Problem 50RE ### 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
1 views

# Evaluating a Definite Integral using a Geometric Formula In Exercises 47–50, sketch the region whose area is represented by the definite integral. Then use a geometric formula to evaluate the integral. ∫ − 2 2 4 − x 2   d x

To determine

To graph: The region whose area represent by definite integral 224x2dx and calculate integration by use of geometrical formula.

Explanation

Given Information:

The provided definite integral is 224x2dx.

Formula used:

Area of circle=πR2

Area of function f(x) bound from x=a and x=b is given by

Area=abf(x)dx

Graph:

Consider the integration,

224x2dx

The integrand function f(x)=4x2

Let x=2,

Substitute, 2 for x in f(x)=4x2.

f(2)=4(2)2=0

Let x=2,

Substitute, 2 for x in f(x)=4x2.

f(2)=4(2)2=0

Let x=0,

Substitute, 0 for x in f(x)=4x2.

f(0)=4(0)2=4=2

The following table represent coordinate of f(x)=4x2.

 Coordinate of x Coordinate of y Coordinate of (x,y) 2 0 (2,0) −2 0 (−2,0) 0 2 (0,2)

The limits of integration from 2 to 2 and integrand is 4x2 represent half circle

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started 