y A - y = f(x) 6. 8. The function f(r) is graphed at right. Write a definite integral (in terms of f) for each of the following quantities. 1. the area bounded by y = 9, x = 6, the graph of f, and the y-axis. 4. 2.
y A - y = f(x) 6. 8. The function f(r) is graphed at right. Write a definite integral (in terms of f) for each of the following quantities. 1. the area bounded by y = 9, x = 6, the graph of f, and the y-axis. 4. 2.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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ChapterA: Appendix
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Question
Transcribed Image Text:yA
8
y = f(x)
6.
4
The function f(r) is graphed at right.
Write a definite integral (in terms of f) for each of the following quantities.
4.
6.
8.
1. the area bounded by y = 9, x = 6, the graph of f, and the y-axis.
2. the area bounded by r = 2, y = r, and the graph of f.
3. the volume of the solid formed when rotating about the r-axis the region described in
Problem 1.
4. the volume of the solid formed when rotating about the y-axis the region described in
Problem 2.
5. the volume of the solid whose base is the region described in Problem 1, if each cross
section perpendicular to the r-axis is an isosceles right triangle with the right angle
located at y = 9. (See figure below.)
typical
cross-section
y=9
1
2.
![6. Choose one of the integrals you wrote above, and approximate it using the Trapezoid
Rule and Simpson's Rule (both with n= 6 subintervals).
7. Choose one of the area integrals from the list above, and approximate it using the
Midpoint Rule with n = 3 subintervals.
In the remaining problems, suppose it is known that
|f"(x)| < 4 on [0, 2],
|f"(x)| < 1 on [2, 4],
|f"(x)| < 3 on [4, 6],
|f"(x)| < 10 on [6, 8], and
|f(4) (x)| < 100 on [0, 8].
8. Is it likely that the M3 approximation for Problem 7 is within 5% of the exact value?
Show all work to justify your conclusion.
What is the minimum number of subintervals n for which the following quantities are
within 10-3 of the exact value?
(a) The T, approximation of the problem 1 area
(b) The Sn approximation of the problem 2 area
Re ference Formulas (deliberately left unlabeled)
klb-a(ax)
(ax)²
K (b-a),
4
24
12
where ox=
180
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfb7e1f8-9732-470d-943a-5f91a132b605%2Fe34e03ff-769f-4823-855f-9360116375ac%2Fk3accxh_processed.png&w=3840&q=75)
Transcribed Image Text:6. Choose one of the integrals you wrote above, and approximate it using the Trapezoid
Rule and Simpson's Rule (both with n= 6 subintervals).
7. Choose one of the area integrals from the list above, and approximate it using the
Midpoint Rule with n = 3 subintervals.
In the remaining problems, suppose it is known that
|f"(x)| < 4 on [0, 2],
|f"(x)| < 1 on [2, 4],
|f"(x)| < 3 on [4, 6],
|f"(x)| < 10 on [6, 8], and
|f(4) (x)| < 100 on [0, 8].
8. Is it likely that the M3 approximation for Problem 7 is within 5% of the exact value?
Show all work to justify your conclusion.
What is the minimum number of subintervals n for which the following quantities are
within 10-3 of the exact value?
(a) The T, approximation of the problem 1 area
(b) The Sn approximation of the problem 2 area
Re ference Formulas (deliberately left unlabeled)
klb-a(ax)
(ax)²
K (b-a),
4
24
12
where ox=
180
2
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