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To solve: The function is defined on the interval ,
a. Graph .
In (b)–(e), approximate the area under from 0 to 3 as follows:
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Answer to Problem 12AYU
a.
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
a. Graph
To solve: The function is defined on the interval ,
b. Partition into three subintervals of equal length and choose as the left endpoint of each subinterval.
![Check Mark](/static/check-mark.png)
Answer to Problem 12AYU
b. 18
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
b. Partition into three subintervals of equal length 1 and choose as the left endpoint of each subinterval.
The area is approximated as
To solve: The function is defined on the interval ,
c. Partition into three subintervals of equal length and choose as the right endpoint of each subinterval.
![Check Mark](/static/check-mark.png)
Answer to Problem 12AYU
c. 12
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
c. Partition into three subintervals of equal length 1 and choose as the right endpoint of each subinterval.
The area is approximated as
To solve: The function is defined on the interval ,
d. Partition into six subintervals of equal length and choose as the left endpoint of each subinterval.
![Check Mark](/static/check-mark.png)
Answer to Problem 12AYU
d.
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
d. Partition into six subintervals of equal length and choose as the left endpoint of each subinterval.
The area is approximated as
To solve: The function is defined on the interval ,
e. Partition into six subintervals of equal length and choose as the right endpoint of each subinterval.
![Check Mark](/static/check-mark.png)
Answer to Problem 12AYU
e.
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
e. Partition into six subintervals of equal length and choose as the right endpoint of each subinterval.
The area is approximated as
To solve: The function is defined on the interval ,
f. What is the actual area ?
![Check Mark](/static/check-mark.png)
Answer to Problem 12AYU
f. 12
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
f. The actual area under the graph of from 0 to 3 is the area of a right triangle whose base is of length 3 and whose height is 8. The actual area is
Therefore
Chapter 14 Solutions
Precalculus Enhanced with Graphing Utilities
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