   Chapter 13.3, Problem 13E ### 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. f ( x ) = x 2 + 2 ; g ( x ) = − x 2 ; x = 0 ; x = 2

To determine

To calculate: The area of the region bounded by equation f(x)=x2+2 and g(x)=x2 from x=0 to x=2.

Explanation

Given information:

The provided equation are:

f(x)=x2+2, g(x)=x2 from x=0 to x=2.

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,

f(x)=x2+2

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

Substitute x=0 in the function f(x)=x2+2.

y=(02+2)=2

Substitute x=1 in the function f(x)=x2+2.

y=(12+2)=3

Substitute x=2 in the function f(x)=x2+2.

y=(22+2)=6

Substitute x=1 in the function f(x)=x2+2.

y=((1)2+2)=3

The following table shows the different coordinate (x,y) for equation f(x)=x2+2.

 x f(x)=x2+2 Coordinates (x,y) 0 2 (0,2) 1 3 (1,3) 2 6 (2,6) −1 3 (−1,3)

Now, consider,

g(x)=x2

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

y=(0)2=0

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

y=(1)2=1

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

y=(2)2=4

Substitute x=1 in the function g(x)=x2

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