3. Consider the closed Newton-Cotes formula with n = 4 (Boole's rule): b a I(f) 14,closed (f) = 90 [7f (a) +32f(a + h) + 12f(a + 2h) + 32f(a+3h) + 7ƒ(b)] where h = (ba)/4. (a) Find the degree of precision. (b) Derive the error term associated with this quadrature rule. [Hint: Use the theorem for the error term from the notes.] (c) Approximate the value of the definite integral 2 d using this rule. X
3. Consider the closed Newton-Cotes formula with n = 4 (Boole's rule): b a I(f) 14,closed (f) = 90 [7f (a) +32f(a + h) + 12f(a + 2h) + 32f(a+3h) + 7ƒ(b)] where h = (ba)/4. (a) Find the degree of precision. (b) Derive the error term associated with this quadrature rule. [Hint: Use the theorem for the error term from the notes.] (c) Approximate the value of the definite integral 2 d using this rule. X
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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![3. Consider the closed Newton-Cotes formula with n = 4 (Boole's rule):
b
a
I(f) 14,closed (f)
=
90
[7f (a) +32f(a + h) + 12f(a + 2h) + 32f(a+3h) + 7ƒ(b)]
where h = (ba)/4.
(a) Find the degree of precision.
(b) Derive the error term associated with this quadrature rule. [Hint: Use the theorem for the
error term from the notes.]
(c) Approximate the value of the definite integral 2 d using this rule.
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91f76606-a4d9-42f0-be0d-7b1366a5593f%2Fe8b7aad1-b8b5-4a71-ace9-cd0b86a3c9bb%2Fx0kbilc_processed.png&w=3840&q=75)
Transcribed Image Text:3. Consider the closed Newton-Cotes formula with n = 4 (Boole's rule):
b
a
I(f) 14,closed (f)
=
90
[7f (a) +32f(a + h) + 12f(a + 2h) + 32f(a+3h) + 7ƒ(b)]
where h = (ba)/4.
(a) Find the degree of precision.
(b) Derive the error term associated with this quadrature rule. [Hint: Use the theorem for the
error term from the notes.]
(c) Approximate the value of the definite integral 2 d using this rule.
X
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