   Chapter 13.3, Problem 19E ### 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. h ( x ) = x 2 ;   k ( x ) = x

To determine

To calculate: The area of the region between h(x)=x2 and k(x)=x.

Explanation

Given information:

The provided curve is:

h(x)=x2 and k(x)=x.

Formula used:

Area between two curve:

If f and g are continuous functions on [a,b] and if f(x)g(x) on [a,b], then the area of the region bounded by y=f(x), y=g(x), x=a, and x=b is:

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

Or

A=Integral of (Top Bottom)

Calculation:

Consider the provided equation:

h(x)=x2 and k(x)=x

Draw the graph of the above function to check whether h(x)k(x):

Calculate the values at different values of x:

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

y=(0)2=0

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

y=(1)2=1

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

y=(2)2=4

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

y=(1)2=1

The table provided below shows the values of the function at different values of x.

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

Now, consider k(x)=x

Substitute x=0 in the function k(x)=x.

y=0=0

Substitute x=1 in the function k(x)=x.

y=1=1

Substitute x=2 in the function k(x)=x.

y=2=1.41

Substitute x=1 in the function k(x)=x

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