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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 + 3 x 2 + 1 , g ( x ) = x + 4

To determine

To calculate: The area of the region bounded by the graphs of the functions f(x)=x3+3x2+1,g(x)=x+4.

Explanation

Given information:

The functions are f(x)=x3+3x2+1,g(x)=x+4.

Formula used:

Area of the region bounded by two graphs:

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

Calculate:

Consider the functions f(x)=x3+3x2+1,g(x)=x+4.

First make a table for the function f(x)=x3+3x2+1

x f(x)=x3+3x2+1 (x,f(x))
3 f(3)=(3)3+3(3)2+1=1 (3,1)
1 f(1)=(1)3+3(1)2+1=3 (1,3)
1 f(1)=(1)3+3(1)2+1=5 (1,5)

Now, take the second function g(x)=x+4

Make a table for this given function

x g(x)=x+4 (x,g(x))
3 g(3)=(3)+4=1 (3,1)
1 g(1)=(1)+4=3 (1,3)
1 g(1)=(1)+4=5 (1,5)

The required graph is shown below:

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