Explanation Given: An integral is given as ∫ 1 5 d t t with number of subintervals n = 8 . Formula used: Simpson’s rule to approximate integral is given by: ∫ a b f ( x ) d x ≈ Δ x 3 [ f ( x 0 ) + 4 ( f ( x 1 ) + f ( x 3 ) + ... + f ( x n − 1 ) ) + 2 ( f ( x 2 ) + f ( x 4 ) + ... + 2 f ( x n − 2 ) ) + f ( x n ) ] Where Δ x = b − a n Concept used: The natural logarithm function is defined by ∫ 1 x 1 t d t = ln x , x > 0 Calculation: The given integral is ∫ 1 5 d t t . Here, a = 1 , b = 5 , n = 8 Therefore, Δ t = b − a n = 5 − 1 8 = 4 8 = 1 2 Now, divide the interval [ 1 , 5 ] into n = 8 subintervals of length Δ t = 1 2 , with the following endpoints: a = 1 , 3 2 , 2 , ..

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 5.9, Problem 56PS

To determine

To calculate: The value of the given integration by Simpson’s Rule for the specified number of intervals.

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Chapter 5.9, Problem 55PS

Chapter 5.9, Problem 57PS

Chapter 5 Solutions

Calculus

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The value of the given integration by Simpson’s Rule for the specified number of intervals.

Solution Summary: The author calculates the value of the given integration by Simpson's Rule for the specified number of intervals. The error is given by E_8=0.001408648412

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To calculate: The value of the given integration by Simpson’s Rule for the specified number of intervals.

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Chapter 5 Solutions