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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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In Exercises 16-19, sketch the region bounded by the graphs of the functions and find the area of the region.

f ( x ) = x 3 , g ( x ) = x 2

To determine

To calculate: The area of the region bounded by the graphs of the functions f(x)=x3,g(x)=x2.

Explanation

Given information:

The functions are f(x)=x3,g(x)=x2.

Formula used:

Area of the region bounded by two graphs:

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

Calculate:

Consider the functions f(x)=x3,g(x)=x2.

First make a table for the function f(x)=x3

x f(x)=x3 (x,f(x))
0 f(0)=03=0 (0,0)
1 f(1)=13=1 (1,1)
8 f(8)=83=2 (8,2)

Now, take the second function g(x)=x2

Make a table for this given function

x g(x)=x2 (x,g(x))
0 g(0)=(0)2=0 (0,0)
1 g(1)=(1)2=1 (1,1)
2 g(2)=(2)2=4 (2,4)

The required graph is shown below:

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