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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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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 4 x , y = x 2 2 x

To determine

To graph: The area of the region bounded by the graphs of the functions y=x34x,y=x22x also find the area of the region.

Explanation

Given information:

The functions are y=x34x,y=x22x.

Graph:

Consider the functions y=x34x,y=x22x.

First make a table for the function y=x34x,

x y=x34x (x,y)
2 y=(2)34(2)=0 (2,0)
0 y=(0)34(0)=0 (0,0)
1 y=(1)34(1)=3 (1,3)

Now, take the second function y=x22x.

Make a table for this given function,

x y=x22x (x,y)
2 y=(2)22(2)=0 (2,0)
0 y=(0)22(0)=0 (0,0)
1 y=(1)22(1)=3 (1,3)

The required graph is shown below:

Because the value of a and b are not given so, finding the x-coordinates of the points of intersection of the two graphs. To do this equate the two functions and solve for x.

x34x=x22xx3+x22x=0

Further simplify,

x(x2+x2)=0x(x+2)(x1)=0x=0,2,1

Therefore, the value of a and b in first part are 2 and 0 and in second part it will change from 0 to 1 respectively

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