(b) Approximate the definite integral f"/² cos(x)dx by employing the Composed Midpoint rule with n = 4.
(b) Approximate the definite integral f"/² cos(x)dx by employing the Composed Midpoint rule with n = 4.
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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Part B
![Question 5
Consider f e C²[a,b], n even, h = -, x; = a + (j+1)h, j = -1,0, 1, ·..n + 1, and p e (a, b). The error
term in the Composite Midpoint rule is:
b — а
(a)
Determine the values of n and h that will ensure an approrimation error of less that 10-5
T/2
when approrimating S cos(x)dx and using the Composed Midpoint rule.
(b)
Approximate the definite integral f² cos(x)dx by employing the Composed Midpoint rule with
n = 4.
Page 7](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc6748d3-4cd8-403e-abcc-dc83fd70c599%2Fd707ed91-b1ba-41cc-8c92-f13e3d01ea02%2Fv78etas_processed.png&w=3840&q=75)
Transcribed Image Text:Question 5
Consider f e C²[a,b], n even, h = -, x; = a + (j+1)h, j = -1,0, 1, ·..n + 1, and p e (a, b). The error
term in the Composite Midpoint rule is:
b — а
(a)
Determine the values of n and h that will ensure an approrimation error of less that 10-5
T/2
when approrimating S cos(x)dx and using the Composed Midpoint rule.
(b)
Approximate the definite integral f² cos(x)dx by employing the Composed Midpoint rule with
n = 4.
Page 7
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