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Repeat Problem 9 for .
![Check Mark](/static/check-mark.png)
To solve: The function is defined on the interval ,
a. Graph .
In (b)-(e), approximate the area under from 0 to 6 as follows:
Answer to Problem 10AYU
a.
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
; ; ; ; ; ;
a. Graph .
![Check Mark](/static/check-mark.png)
To solve: The function is defined on the interval ,
b. Partition into three subintervals of equal length 2 and choose as the left endpoint of each subinterval.
Answer to Problem 10AYU
b. 48
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
![Check Mark](/static/check-mark.png)
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.
Answer to Problem 10AYU
c. 96
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
![Check Mark](/static/check-mark.png)
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.
Answer to Problem 10AYU
d. 60
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
![Check Mark](/static/check-mark.png)
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.
Answer to Problem 10AYU
e. 84
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
![Check Mark](/static/check-mark.png)
To solve: The function is defined on the interval ,
f. What is the actual area ?
Answer to Problem 10AYU
f. 72
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 24. The actual area is
Therefore
Chapter 14 Solutions
Precalculus Enhanced with Graphing Utilities
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