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ere exists a µ e (a, b) for which the Composite Šimpson' written with its error term as (n/2)-1 n/2 f(x) dx f(a) + 2 f(x2;) +4f (x2j–1) +

ere exists a µ e (a, b) for which the Composite Šimpson' written with its error term as (n/2)-1 n/2 f(x) dx f(a) + 2 f(x2;) +4f (x2j–1) +

Advanced Engineering Mathematics
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 the approximation obtained from Rk,2 is the same as that given by the Composite Simpson’s rule described in Theorem 4.4 with h = hk.

Theorem 4 uploaded for reference

Let f e C*[a, b], n be even, h = (b – a)/n, and x; = a + jh, for each j = 0,1,...,n. There exists a u e (a,b) for which the Composite Simpson's rule for n subintervals can be written with its error term as (n/2)–1 n/2 h f(x) dx = f(a) +2 E fx2;) + 4£f(nj-1) + f (b) b-a f(). 180 j=1 j=l
Transcribed Image Text:Let f e C*[a, b], n be even, h = (b – a)/n, and x; = a + jh, for each j = 0,1,...,n. There exists a u e (a,b) for which the Composite Simpson's rule for n subintervals can be written with its error term as (n/2)–1 n/2 h f(x) dx = f(a) +2 E fx2;) + 4£f(nj-1) + f (b) b-a f(). 180 j=1 j=l
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