Explanation Given information: ∫ − 1 1 1 + x 4 d x with n = 4 where n is the number of equal subintervals. Formula used: Simpson’s Rule: ∫ a b f ( x ) d x ≈ [ f ( a 0 ) + 4 f ( x 1 ) + 2 f ( a 1 ) + 4 f ( x 2 ) + 2 f ( a 2 ) + ⋯ + 2 f ( a n − 1 ) + 4 f ( x n ) + f ( a n ) ] Δ x 6 Calculation: For n = 4 , Δ x = b − a n = 1 − ( − 1 ) 4 = 0.5 The end points of the intervals begin at a = − 1 and length of each subinterval is 0.5 . So, the end points of intervals are a 0 = − 1 , a 1 = − 0.5 , a 2 = 0 , a 3 = 0.5 and a 4 = 1 The first midpoint is at a + Δ x 2 = − 1 + 0.5 2 = − 0.75 ⇒ x 1 = − 0.75 The midpoints are also spaced 0.5 units apart. Thus, the midpoints are x 1 = − 0.75 , x 2 = − 0.25 , x 3 = 0.25 and x 4 = 0.75 According to Simpson’s rule, the integral is ∫ − 1 1 1 + x 4 d x ≈ 0

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ISBN: 9780137590810

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar, William Edward Tavernetti

Publisher: PEARSON

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Chapter 9.4, Problem 24E

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To calculate: The approximate value of the integral ∫−111+x4 dx by Simpson’s rule with n=4 where n is the number of equal subintervals, and express the answer to five decimal places.

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Chapter 9.4, Problem 23E

Chapter 9.4, Problem 25E

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The approximate value of the integral ∫ − 1 1 1 + x 4 d x by Simpson’s rule with n = 4 where n is the number of equal subintervals, and express the answer to five decimal places.

Solution Summary: The author calculates the approximate value of the integral by Simpson's rule with n=4.

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To calculate: The approximate value of the integral ∫−111+x4 dx by Simpson’s rule with n=4 where n is the number of equal subintervals, and express the answer to five decimal places.

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Chapter 9 Solutions