Explanation Given Information: The provided integral is ∫ 1 3 ( x ln x ) d x with n = 4 subintervals. Formula used: The Trapezoidal Rule for function f on the interval [ a , b ] is, ∫ a b f ( x ) d x ≈ h 2 [ f ( x 0 ) + 2 f ( x 1 ) + ⋯ + 2 f ( x n − 1 ) + f ( x n ) ] Where, h = b − a n and n is the number of equal subdivisions of [ a , b ] . Calculation: Consider the integral, ∫ 1 3 ( x ln x ) d x The number of subdivisions is n = 4 and the value of a and b are 1 and 3 respectively. The function is, f ( x ) = x ln x By Trapezoidal Rule, ∫ a b f ( x ) d x = h 2 [ f ( x 0 ) + 2 f ( x 1 ) + ..... + 2 f ( x n − 1 ) + f ( x n ) ] The value of h is, h = b − a n = 3 − 1 4 = 0

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, Problem 15T

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To calculate: The value of ∫13(xlnx)dx for n=4 subintervals by the use of the Trapezoidal Rule.

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Chapter 13, Problem 14T

Chapter 13, Problem 16T

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Chapter 13 Solutions

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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The value of ∫ 1 3 ( x ln x ) d x for n = 4 subintervals by the use of the Trapezoidal Rule.

Solution Summary: The author calculates the value of the Trapezoidal Rule for f for n=4 subintervals.

To calculate: The value of ∫13(xlnx)dx for n=4 subintervals by the use of the Trapezoidal Rule.

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Chapter 13 Solutions