Consider the following functionexp (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] toeach 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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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.

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 For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.CR: Chapter 9 Review

Problem 54CR

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Question

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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