   Chapter 13, Problem 21RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find the area between the curves in Problems 19-22. y = x 3  and  y = x  from  x = − 1  to  x = 0

To determine

To calculate: The area under the graph of y=x3 and y=x from x=1 to x=0 using the definite integral method.

Explanation

Given Information:

The provided functions are y=x3 and y=x and range of x is 1x0.

Formula Used:

The area between two graphs:

If f(x)g(x) for all x in [a,b] (so that the graph of f doesn’t move below that of g), then the area of the region between the graphs of f and g and between x=a and x=b is given by:

A=ab[f(x)g(x)dx]

Calculation:

The provided functions are y=x3 and y=x and range of x is 1x0.

The point of intersection can be obtained by keeping them equal:

x3=xx3x=0x(x21)=0

Therefore, x=0 or x21=0.

That is, x=0 or x=1 or x=1

Substitute x=0 in the equation y=x.

y=x=0

Now, substitute x=1 in the equation y=x.

y=x=1

Now, substitute x=1 in the equation y=x.

y=x=1

Therefore, both graphs intersect at points (0,0), (1,1) and (1,1).

Consider the equation y=x3.

Substitute x=0 in y=x3.

y=(0)3=0

Substitute x=2 in y=x3.

y=(2)3=8

Substitute x=2 in y=x3.

y=(2)3=8

Summarized all points in a table,

 x y (x, y) 0 0 (0,0) 2 8 (2,8) −2 −8 (−2,−8)

Now, consider the equation y=x.

Substitute x=0 in y=x.

y=(0)=0

Substitute x=2 in y=x

### 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

#### Expand each expression in Exercises 122. (x+yxy)2

Finite Mathematics and Applied Calculus (MindTap Course List)

#### Evaluate the limit, if it exists. limx4x2+3xx2x12

Single Variable Calculus: Early Transcendentals, Volume I

#### True or False: The slope of a tangent line may be interpreted as average velocity.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 