   Chapter 13, Problem 20RE ### 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 2  and  y = 4 x + 5

To determine

To calculate: The area under the graph of y=x2 and y=4x+5 using the definite integral method.

Explanation

Given Information:

The provided functions are y=x2 and y=4x+5.

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=x2 and y=4x+5.

The points can be obtained by keeping them equal:

x2=4x+5x24x5=0x25x+x5=0x(x5)+1(x5)=0

Further simplify,

x(x5)+1(x5)=0(x+1)(x5)=0

Therefore, x=1 or x=5.

Substitute x=1 in the equation y=x2.

y=x2=(1)2=1

Now, substitute x=5 in the equation y=x2.

y=x2=(5)2=25

Therefore, both graphs intersect at points (1,1) and (5,25).

Consider the equation y=x2.

The graph is obtained as follows:

Substitute x=0 in y=x2.

y=(0)2=0

Substitute x=1 in y=x2.

y=(1)2=1

Substitute x=3 in y=x2.

y=(3)2=9

Summarized all points in a table,

 x y (x,y) 0 0 (0,0) 1 1 (1,1) 3 9 (3,9)

Now, consider the equation y=4x+5,

Substitute x=0 in y=4x+5.

y=4(0)+5=5

Substitute x=1 in y=4x+5.

y=4(1)+5=9

Substitute x=3 in y=4x+5

### 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 