Explanation Formula used: Simpson’s rule: ∫ a b f ( x ) d x ≈ h 3 ( y 0 + 4 y 1 + 2 y 2 + 4 y 3 + 2 y 4 + ⋯ + 4 y n − 1 + y n ) , where h = b − a n . Calculation: The area of the curve is given by the function y = x 2 x 2 + 1 3 . Thus, the area is defined by ∫ 1 4 x 2 x 2 + 1 3 d x , n = 6 . Divide the interval from x = 1 to x = 4 into six intervals. The value of h = 4 − 1 6 = 3 6 = 0.5 . Thus, the intervals are: 1 , 1.5 , 2 , 2.5 , 3 , 3.5 , 4 . Find the values of y 0 , y 1 , ⋯ and tabulate as follows. n x n y n 0 1 1 2 ( 1 ) 2 + 1 3 = 3 3 1 1.5 ( 1.5 ) 2 ( 1.5 ) 2 + 1 3 = ( 1.5 ) 2 ( 2.25 ) + 1 3 = 1.5 5.5 3 2 2 2 2 ( 2 ) 2 + 1 3 = 2 9 3 3 2.5 ( 2.5 ) 2 ( 2.5 ) 2 + 1 3 = ( 2.5 ) 2 ( 6

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 25, Problem 57RE

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To approximate: The area under the curve between x=1 and x=4 by using the Simpson’s rule with n = 6.

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Chapter 25, Problem 56RE

Chapter 25, Problem 58RE

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Chapter 25 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 25.1 - Find an antiderivative of x3 + 4x. Ch. 25.1 - Prob. 2PE Ch. 25.1 - Prob. 1E Ch. 25.1 - Prob. 2E Ch. 25.1 - Prob. 3E Ch. 25.1 - Prob. 4E Ch. 25.1 - In Exercises 5–12, determine the value of a that...Ch. 25.1 - Prob. 6E Ch. 25.1 - Prob. 7E Ch. 25.1 - Prob. 8E

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To approximate: The area under the curve between x = 1 and x = 4 by using the Simpson’s rule with n = 6.

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To approximate: The area under the curve between x=1 and x=4 by using the Simpson’s rule with n = 6.

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Chapter 25 Solutions