Estimate the area of the region bounded by the graph of f(x) = x² +8 and the x-axis on [0,2] in the following ways. a. Divide [0,2] into n = 4 subintervals and approximate the area of the region using a left Riemann sum. Illustrate the solution geometrically. b. Divide [0,2] into n = 4 subintervals and approximate the area of the region using a right Riemann sum. Illustrate the solution geometrically. a. The left Riemann sum is (Type an integer or decimal rounded to three decimal places as needed.) Sketch the graph off and the rectangles used in the left Riemann sum. Choose the correct graph below. O A. 15- O A. X 15- 2.4 Q 2.4 Q B. 5 15- B. 2.4 b. The right Riemann sum is (Type an integer or decimal rounded to three decimal places as needed.) Sketch the graph of f and the rectangles used in the right Riemann sum. Choose the correct graph below. 15- Q 2.4 5 Q C. 5 15- C. 15- 2.4 0 2.4 5
Estimate the area of the region bounded by the graph of f(x) = x² +8 and the x-axis on [0,2] in the following ways. a. Divide [0,2] into n = 4 subintervals and approximate the area of the region using a left Riemann sum. Illustrate the solution geometrically. b. Divide [0,2] into n = 4 subintervals and approximate the area of the region using a right Riemann sum. Illustrate the solution geometrically. a. The left Riemann sum is (Type an integer or decimal rounded to three decimal places as needed.) Sketch the graph off and the rectangles used in the left Riemann sum. Choose the correct graph below. O A. 15- O A. X 15- 2.4 Q 2.4 Q B. 5 15- B. 2.4 b. The right Riemann sum is (Type an integer or decimal rounded to three decimal places as needed.) Sketch the graph of f and the rectangles used in the right Riemann sum. Choose the correct graph below. 15- Q 2.4 5 Q C. 5 15- C. 15- 2.4 0 2.4 5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Estimate the area of the region bounded by the graph of f(x) = x² +8 and the x-axis on [0,2] in the following ways.
a. Divide [0,2] into n = 4 subintervals and approximate the area of the region using a left Riemann sum. Illustrate the
solution geometrically.
b. Divide [0,2] into n = 4 subintervals and approximate the area of the region using a right Riemann sum. Illustrate the
solution geometrically.
a. The left Riemann sum is
(Type an integer or decimal rounded to three decimal places as needed.)
Sketch the graph of f and the rectangles used in the left Riemann sum. Choose the correct graph below.
O A.
15-
O A.
2.4
15-
Q
2.4
N
B.
5
15-
B.
X
15-
2.4
b. The right Riemann sum is
(Type an integer or decimal rounded to three decimal places as needed.)
Sketch the graph of f and the rectangles used in the right Riemann sum. Choose the correct graph below.
N
2.4
C.
Ay
선
15-
0
C.
15-
0
2.4
O
N
2.4
Q
N](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb1d4b9fa-8e97-4733-bef2-752adead349a%2Fe443255b-19ab-40cd-8d06-3c027887ff83%2Fmwo4u5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Estimate the area of the region bounded by the graph of f(x) = x² +8 and the x-axis on [0,2] in the following ways.
a. Divide [0,2] into n = 4 subintervals and approximate the area of the region using a left Riemann sum. Illustrate the
solution geometrically.
b. Divide [0,2] into n = 4 subintervals and approximate the area of the region using a right Riemann sum. Illustrate the
solution geometrically.
a. The left Riemann sum is
(Type an integer or decimal rounded to three decimal places as needed.)
Sketch the graph of f and the rectangles used in the left Riemann sum. Choose the correct graph below.
O A.
15-
O A.
2.4
15-
Q
2.4
N
B.
5
15-
B.
X
15-
2.4
b. The right Riemann sum is
(Type an integer or decimal rounded to three decimal places as needed.)
Sketch the graph of f and the rectangles used in the right Riemann sum. Choose the correct graph below.
N
2.4
C.
Ay
선
15-
0
C.
15-
0
2.4
O
N
2.4
Q
N
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