Derive the Simpson rule with a pair of slices with an equal interval by using the Taylor expansion of f (x) around x, in the region [x¡-1,X¡+1] and the three-point formulas for the first-order and second-order derivatives. Show that the contribution of the last slice is also correctly given by the formulas in the above discussion.

Computer Networking: A Top-Down Approach (7th Edition)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
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Chapter1: Computer Networks And The Internet
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1. Develop a program that can calculate the integral with a given integrand f(x) in the
region [a, b] by the Simpson rule with nonuniform data points. Check its accuracy with
the integral e*dx with x, = jhei“, where h and a are small constants.
2. Derive the Simpson rule with a pair of slices with an equal interval by using the Taylor
expansion of f (x) around x, in the region [x;-1, X¡+1] and the three-point formulas for
the first-order and second-order derivatives. Show that the contribution of the last
slice is also correctly given by the formulas in the above discussion.
Transcribed Image Text:1. Develop a program that can calculate the integral with a given integrand f(x) in the region [a, b] by the Simpson rule with nonuniform data points. Check its accuracy with the integral e*dx with x, = jhei“, where h and a are small constants. 2. Derive the Simpson rule with a pair of slices with an equal interval by using the Taylor expansion of f (x) around x, in the region [x;-1, X¡+1] and the three-point formulas for the first-order and second-order derivatives. Show that the contribution of the last slice is also correctly given by the formulas in the above discussion.
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