   Chapter 13.3, Problem 18E ### 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

# In Problems 13-26, equations are given whose graphs enclose a region. In each problem, find the area of the region. y = x 2 ;   y = 4 x − x 2

To determine

To calculate: The area of the region between y=x2 and y=4xx2.

Explanation

Given information:

The provided curve is:

y=x2 and y=4xx2

Formula used:

The area of the region bounded by equation y=f(x) and y=g(x) from x=a to x=b is given by

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

Here, f(x) and g(x) are continuous functions on [a,b] and if f(x)g(x) on [a,b].

Calculation:

Consider the equation,

y(x)=x2

Calculate the values y(x) at different values of x,

Substitute x=0 in the function y(x)=x2.

y(0)=(0)2=0

Substitute x=1 in the function y(x)=x2.

y(1)=(1)2=1

Substitute x=2 in the function y(x)=x2.

y(2)=(2)2=4

Substitute x=1 in the function y(x)=x2.

y(1)=(1)2=1

The following table shows the different coordinate (x,y) for equation y(x)=x2.

 x y(x)=x2 Coordinates (x,y) 0 0 (0,0) 1 1 (1,1) 2 4 (2,4) −1 1 (−1,1)

Now, consider

y(x)=4xx2

Substitute x=0 in the function y(x)=4xx2.

y=4(0)(0)2=0

Substitute x=1 in the function y(x)=4xx2.

y=4(1)(1)2=3

Substitute x=2 in the function y(x)=4xx2.

y=4(2)(2)2=4

Substitute x=1 in the function y(x)=4xx2.

y=4(1)(1)2=5

The following table shows the different coordinate (x,y) for equation y(x)=4xx2

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