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To solve: The function is defined on the interval ,
a. Graph ,
indicating the area under from 0 to 4.
![Check Mark](/static/check-mark.png)
Answer to Problem 18AYU
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. Approximate the area by Partition into four subintervals of equal length and choose as the left endpoint of each subinterval.
![Check Mark](/static/check-mark.png)
Answer to Problem 18AYU
b.
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
b. Partition into four 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. Approximate the area by Partition into eight subintervals of equal length and choose as the left endpoint of each subinterval.
![Check Mark](/static/check-mark.png)
Answer to Problem 18AYU
c.
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
c. Partition into eight 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 ,
d. Express the area as an integral.
![Check Mark](/static/check-mark.png)
Answer to Problem 18AYU
d.
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
d. Express the area as an integral
The area as an integral is
To solve: The function is defined on the interval ,
e. Use a graphing utility to approximate the integral.
![Check Mark](/static/check-mark.png)
Answer to Problem 18AYU
e.
Explanation of Solution
Given:
The function is defined on the interval .
Calculation:
e. Use a graphing utility to approximate the integral.
That is evaluate the integral
The value of the integral is
so the area under the graph of from 0 to 4 is .
Chapter 14 Solutions
Precalculus
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