Consider the following table of function values. X 0.0 7.4 2.0 8.3 0.4 0.8 1.2 1.6 f(x) X f(x) 3.2 8.9 2.4 8.6 8.7 2.8 7.6 8.6 3.2 8.4 8.9 (a) Use the Midpoint Rule with n = 4 and the given data to estimate the value of the integral. (Round your answer to two decimal places.) 1³ Jo f(x) dx (b) Suppose it is known that -5 ≤ f"(x) ≤ 2 for all x. Estimate the error involved in the approximation in part (a). (Round your answer to four decimal places.)
Consider the following table of function values. X 0.0 7.4 2.0 8.3 0.4 0.8 1.2 1.6 f(x) X f(x) 3.2 8.9 2.4 8.6 8.7 2.8 7.6 8.6 3.2 8.4 8.9 (a) Use the Midpoint Rule with n = 4 and the given data to estimate the value of the integral. (Round your answer to two decimal places.) 1³ Jo f(x) dx (b) Suppose it is known that -5 ≤ f"(x) ≤ 2 for all x. Estimate the error involved in the approximation in part (a). (Round your answer to four decimal places.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Transcribed Image Text:Consider the following table of function values.
X
0.0
0.4
0.8
1.2
1.6
f(x) x f(x)
7.4 2.0 8.3
3.2
8.9 2.4 8.6
8.7 2.8
8.6 3.2 8.4
8.9
7.6
(a) Use the Midpoint Rule with n = 4 and the given data to estimate the value of the integral. (Round your answer to two decimal places.)
f(x) dx
(b) Suppose it is known that −5 ≤ f"(x) ≤ 2 for all x. Estimate the error involved in the approximation in part (a). (Round your answer to four decimal places.)
-
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 10 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
