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Chapter 4: 46 (page 386)

f(x)=x2-x-1,g(x)=5-x2,[-2,3]

Short Answer

Expert verified

The exact area between the graphs is 92or 4.5square units.

Step by step solution

01

Given information

f(x)=x2-x-1,g(x)=5-x2,[-2,3]

02

Calculation

Consider the following functions:

f(x)=x2;g(x)=x+2.

The objective is to find the exact area of the region between the two graphs on the interval [-3,3].

The point of intersection of the two function is,

x2=x+2x2-x-2=0x2-2x+x-2=0x(x-2)+1(x-2)=0(x-2)(x+1)=0x=-1orx=2

The graph is show below,

The exact area of the region is calculated as follows:

role="math" localid="1651079495478" 鈭�-12|f(x)-g(x)|dx=鈭�-12(x+2)-x2dx=鈭�-12(x+2-x2)dx=x22+2x-x33-12=222+2(2)-233-(-1)22+2(-1)-(-1)33

=92or4.5square units.

Therefore, the exact area between the graphs is 92or 4.5square units

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