Explanation Given: An integral is given as ∫ 0 4 d x 1 + x 3 with number of subintervals n = 6 . 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 Calculation: The given integral is ∫ 0 4 d x 1 + x 3 . Here, a = 0 , b = 4 , n = 6 Therefore, Δ x = b − a n = 4 − 0 6 = 4 6 = 2 3 Now, divide the interval [ 0 , 4 ] into n = 6 subintervals of length Δ x = 2 3 , with the following endpoints: a = 0 , 2 3 , 4 3 , 2 , 8 3 , 10 3 , 4 = b Evaluate the following functional values at these endpointsfor Simpson’s Rule: f ( x 0 ) = f ( a ) = f ( 0 ) = 1 4 f ( x 1 ) = 4 f ( 2 3 ) = 4 ⋅ 1 1 + ( 2 3 ) 3 = 3

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 5, Problem 29CRP

To determine

To calculate: The approximated value of the given integration by Simpson’s Rulel.

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Chapter 5, Problem 28CRP

Chapter 5, Problem 30CRP

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Calculus

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The approximated value of the given integration by Simpson’s Rulel.

Solution Summary: The author calculates the approximated value of the given integration by Simpson's Rulel.

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To calculate: The approximated value of the given integration by Simpson’s Rulel.

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Chapter 5 Solutions