(a) Explanation To develop the Trapezoidal rule formula, it is always assumed that f ( x ) ≥ 0 on [ a , b ] and then subdivide the interval [ a , b ] into n equal pieces, each of length b − a n . Within each subdivision, area is approximated using trapezoid. Thus, since there are no pairs and also, the divisions are n equal pieces, so the number of divisions can be both even and odd. For example, consider the provided integral, ∫ 0 1 4 d x x 2 + 1 d x And the value of n is 5 which is odd. And, a = 0 , b = 1 For each interval [ a , b ] and value of n , h = b − a n And, x n = a + n h By using the above formula, h = 1 − 0 5 = 1 5 i x i = a + i h f ( x i ) = 4 x 2 + 1 0 0 4 1 0 (b) To determine Whether the provided statement “When the Simpson’s rule is used, the number of subdivisions, n , must be even.”

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 13.8, Problem 2CP

(a)

To determine

Whether the provided statement “When the Trapezoidal rule is used, the number of subdivisions, n, must be even.”

(b)

To determine

Whether the provided statement “When the Simpson’s rule is used, the number of subdivisions, n, must be even.”

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Chapter 13.8, Problem 1CP

Chapter 13.8, Problem 3CP

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Mathematical Applications for the Management, Life, and Social Sciences

Ch. 13.1 - CHECKPOINT 1. For the interval [0, 2]. determine...Ch. 13.1 - Prob. 2CP Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E

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Whether the provided statement “When the Trapezoidal rule is used, the number of subdivisions, n , must be even.”

Solution Summary: The author explains that the statement "When the Trapezoidal rule is used, the number of subdivisions, n, must be even." is false.