IVx + 2 – a| dx 0,

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.7: Operations On Functions
Problem 2E
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Question

Evaluate the integral (by interpreting it as the area between two curves)

 

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4
|yx + 2 - x| da
Transcribed Image Text:4 |yx + 2 - x| da
Expert Solution
Step 1

Consider the given integral:

04x+2-xdx

Here, the objective is to evaluate the given integral.

Step 2

Let fx=x+2-x, it can be written as piecewise over the interval 0,4

Case I: x+2>x, then fx=x+2-x

To find the value of x, solve 

x+2>xSquare both side since, x>0x+2>x2x2-x-2<0x+1x-2<0

Therefore x-1,2

Case II: x+2<x, then fx=x-x+2

To find the value of x, solve 

x+2<xSquare both side since, x>0x+2<x2x2-x-2>0x+1x-2>0

Therefore x2,

Therefore

fx=x+2-x  ; 0x2x-x+2  ; 2x4

 

 

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