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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 6 as follows:
![Check Mark](/static/check-mark.png)
Answer to Problem 9AYU
Solution:
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 9AYU
Solution:
b. 36
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
; ; ; ; ; ;
b. Partition into three subintervals of equal length 2 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 9AYU
Solution:
c. 72
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
; ; ; ; ; ;
c. Partition into three subintervals of equal length 2 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 9AYU
Solution:
d. 45
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
; ; ; ; ; ;
d. Partition into six 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 ,
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 9AYU
Solution:
e. 63
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
; ; ; ; ; ;
e. Partition into six 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 ,
f. What is the actual area ?
![Check Mark](/static/check-mark.png)
Answer to Problem 9AYU
Solution:
f. 54
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
; ; ; ; ; ;
f. The actual area under the graph of from 0 to 6 is the area of a right triangle whose base is of length 6 and whose height is 18. The actual area is
Therefore
Chapter 14 Solutions
Precalculus Enhanced with Graphing Utilities
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