1. Evaluate the Riemann sum for ƒ(x)=4- x², 0≤x≤ 2, with four subintervals, taking the sample points to be right endpoints. Explain, with the aid of a diagram, what Riemann sum represents.
1. Evaluate the Riemann sum for ƒ(x)=4- x², 0≤x≤ 2, with four subintervals, taking the sample points to be right endpoints. Explain, with the aid of a diagram, what Riemann sum represents.
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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Solve probem 1, 3, and 4 with explanation please.
![The Definite Integral
1. Evaluate the Riemann sum for ƒ(x)=4-x², 0≤x≤2, with four subintervals, taking
the sample points to be right endpoints. Explain, with the aid of a diagram, what
Riemann sum represents.
2. If f(x)=lnx-2, 1≤x≤3, evaluate the Riemann sum with n=4, taking the sample
points to be left endpoints (give your answer correct to six decimal places).
3. If f(x)=√x-1, 0≤x≤3, evaluate the Riemann sum with n=6, taking the sample
points to be midpoints (give your answer correct to six decimal places).
8
4. The graph of a function f is given. Estimate f(x)dx using four subintervals with
(a) right endpoints, (b) left endpoints, and (c) midpoints.
upper estimates for
1
0
0
1
5. A table of values of an increasing function is given. Use the table to find lower and
8
LX]
f(x)dx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F44fc33fa-f0a7-4f0d-8fd2-501707f936b1%2F0d5c12b9-780c-41d1-82b2-30294da59479%2Forkdlq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The Definite Integral
1. Evaluate the Riemann sum for ƒ(x)=4-x², 0≤x≤2, with four subintervals, taking
the sample points to be right endpoints. Explain, with the aid of a diagram, what
Riemann sum represents.
2. If f(x)=lnx-2, 1≤x≤3, evaluate the Riemann sum with n=4, taking the sample
points to be left endpoints (give your answer correct to six decimal places).
3. If f(x)=√x-1, 0≤x≤3, evaluate the Riemann sum with n=6, taking the sample
points to be midpoints (give your answer correct to six decimal places).
8
4. The graph of a function f is given. Estimate f(x)dx using four subintervals with
(a) right endpoints, (b) left endpoints, and (c) midpoints.
upper estimates for
1
0
0
1
5. A table of values of an increasing function is given. Use the table to find lower and
8
LX]
f(x)dx.
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