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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 ) = 6 , g ( x ) = x 2 x 6

To determine

To calculate: The area of the region bounded by the graphs of the functions f(x)=6,g(x)=x2x6.

Explanation

Given information:

The functions are f(x)=6,g(x)=x2x6.

Formula used:

Area of the region bounded by two graphs:

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

Calculation:

Consider the functions f(x)=6,g(x)=x2x6.

The graph of the function f(x)=6 is a horizontal line passing through the point (0,6)

Now make a table for the function g(x)=x2x6

x g(x)=x2x6 (x,g(x))
3 g(3)=(3)2(3)6=6 (3,6)
1 g(1)=(1)2(1)6=6 (1,6)
2 g(2)=(2)2(2)6=4 (2,4)

The required graph is shown below:

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