Explanation Given information: The given integral is ∫ 3 5 ( 9 − x 2 ) d x . The value of N is 4. Formula Used: The integral is in the form of ∫ a b f ( x ) d x . The formula for theSimpson’s rule S N is: S N = 1 3 Δ x ( x 0 + 4 x 1 + 2 x 2 + 4 x 3 + … + 4 x ( N − 1 ) + x N ) Where, Δ x = b − a N and x j = f ( a + j Δ x ) . Calculation: The integral is I = ∫ 3 5 ( 9 − x 2 ) d x . Compare the given integral with ∫ a b f ( x ) d x . So, the function be f ( x ) = 9 − x 2 . And, a = 3 , b = 5 . Find the value of Δ x . Δ x = b − a N = 5 − 3 4 = 2 4 = 0.5 To find the value of S 4 , first find the values of x 0 , x 1 , x 2 , x 3 and x 4 . Substitute 0 for j , 0.5 for Δ x and 3 for a in the formula x j = f ( a + j Δ x ) . x 0 = f ( 3 + 0 ( 0.5 ) ) = f ( 3 ) = 9 − ( 3 ) 2 = 9 − 9 = 0 Substitute 1 for j , 0.5 for Δ x and 3 for a in the formula x j = f ( a + j Δ x ) . x 1 = f ( 3 + 1 ( 0.5 ) ) = f ( 3.5 ) = 9 − ( 3.5 ) 2 = 9 − 12.25 = − 3.25 Substitute 2 for j , 0

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differ…

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Chapter 8.9, Problem 14E

To determine

To calculate:

The value of SN.

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Ch. 8.1 - Prob. 1PQ Ch. 8.1 - Prob. 2PQ Ch. 8.1 - Prob. 3PQ Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

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