   Chapter 5, Problem 89RE ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding the Area Bounded by Two Graphs In Exercises 87-94, sketch the region bounded by the graphs of the functions and find the area of the region. y = ( x − 3 ) 2 , y = 8 − ( x − 3 ) 2

To determine

To graph: The area of the region bounded by the graphs of the functions y=(x3)2,y=8(x3)2 also find the area of the region.

Explanation

Given information:

The functions are y=(x3)2,y=8(x3)2.

Graph:

Consider the functions y=(x3)2,y=8(x3)2.

First make a table for the function y=(x3)2=x26x+9,

 x y=x2−6x+9 (x,y) −1 y=(−1)2−6(−1)+9=16 (−1,16) 1 y=(1)2−6(1)+9=4 (1,4) 2 y=(2)2−6(2)+9=1 (2,1)

Now, take the second function y=8(x3)2x2+6x1,

Make a table for this given function,

 x y=−x2+6x−1 (x,y) −1 y=−(−1)2+6(−1)−1=−8 (−1,−8) 1 y=−(1)2+6(1)−1=4 (1,4) 2 y=−(2)2+6(2)−1=7 (2,7)

The required graph is shown below:

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