Show that if n = 1 in the Newton-Cotes formula, then [ Sº b-a 2 f(x)dx≈ [f(a) + f(b)]
Show that if n = 1 in the Newton-Cotes formula, then [ Sº b-a 2 f(x)dx≈ [f(a) + f(b)]
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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![Show that if n = 1 in the Newton-Cotes formula, then
·b
– a
[ f(x)dx = b = ª (f(a) + f(b)]
2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fb2d316-2402-4377-835d-bb3f3e603de5%2F35bda2bb-f72c-4077-ad05-c8baf01c95c4%2Fo59bfss_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Show that if n = 1 in the Newton-Cotes formula, then
·b
– a
[ f(x)dx = b = ª (f(a) + f(b)]
2
Expert Solution
Step 1
The Newton-Cotes formula on the interval [a,b] is given as
with nodes
where n is a natural number, h=, and the number of nodes is N= n+1.
The coefficients are determined by the formula
.
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