3 1 -1 -2 -3 1 2 3. 4 6 7 Use the graph to compute | f(x)dx. Show all of your work.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 59E
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Below is the graph of y = f(x).

 

3
1
-1
-2
-3
1
3
4
6 7
8.
Use the graph to compute
f (x)dx.
Show all of your work.
Transcribed Image Text:3 1 -1 -2 -3 1 3 4 6 7 8. Use the graph to compute f (x)dx. Show all of your work.
Expert Solution
Step 1

The integral 08f(x)dx represents the area of the region under the graph of f(x) from 0 to 8.

To find the area, split the region into 4 for the convivence. The area of the graph below the x axis is considered as negative.

Therefore,  08f(x)dx=01f(x)dx+14f(x)dx+47f(x)dx+78f(x)dx.

 

Step 2

Find the area of each considering one square  has area of 1 unit.

The area under the x axis is considered as negative.

Thus,

01f(x)=12length×width=121×-3=-32

14f(x)=12length×width=123×1=32

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