You need to show (a) Gaussian nodes and weights (A) transfer from [-1, 1] to each sub-interval (see page 25-Lecture 16) (b) integration for each sub-interval, and (c) sum of integration for each sub-interval.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Consider the following function
exp (т) — еxp(-л')
exp(x) + exp(-т)
+ In(x)
f (x) =
wherer e [1, 5]. Use 5 nodes to uniformly cut the interval [1,5] into 4 sub-
intervals. Truncate the final result to 4 decimal places.
Use 3 Gaussian points (n = 2) to evaluate the integration in each sub-
interval, and sum them up to get the integration over the entire domain.
You need to show (a) Gaussian nodes and weights (A) transfer from [–1,1] to
each sub-interval (see page 25-Lecture 16) (b) integration for each sub-interval,
and (c) sum of integration for each sub-interval.
Transcribed Image Text:Consider the following function exp (т) — еxp(-л') exp(x) + exp(-т) + In(x) f (x) = wherer e [1, 5]. Use 5 nodes to uniformly cut the interval [1,5] into 4 sub- intervals. Truncate the final result to 4 decimal places. Use 3 Gaussian points (n = 2) to evaluate the integration in each sub- interval, and sum them up to get the integration over the entire domain. You need to show (a) Gaussian nodes and weights (A) transfer from [–1,1] to each sub-interval (see page 25-Lecture 16) (b) integration for each sub-interval, and (c) sum of integration for each sub-interval.
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