Explanation Given: An integral is given as ∫ − 1 2 ( x 3 − 3 x + 4 ) d x . Formula used: For any polynomial p ( x ) of degree less than or equal to 3 ∫ a b p ( x ) d x = b − a 6 [ p ( a ) + 4 p ( a + b 2 ) + p ( b ) ] Calculation: Consider the given integral. ∫ − 1 2 ( x 3 − 3 x + 4 ) d x Here the function p ( x ) = x 3 − 3 x + 4 is a polynomial of degree 3. Prismoidal rule can be used to evaluate the integral. a = − 1 , b = 2 The given integral can be evaluated as shown: ∫ − 1 2 ( x 3 − 3 x + 4 ) d x = 2 − ( − 1 ) 6 [ p (

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Question

Chapter 5.8, Problem 55PS

To determine

To calculate: The value of the integral ∫−12(x3−3x+4)dx by Prismoidal rule.

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Chapter 5.8, Problem 54PS

Chapter 5.8, Problem 56PS

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Chapter 5 Solutions

Calculus

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The value of the integral ∫ − 1 2 ( x 3 − 3 x + 4 ) d x by Prismoidal rule.

Solution Summary: The author explains how Prismoidal rule can be used to evaluate the integral.

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To calculate: The value of the integral ∫−12(x3−3x+4)dx by Prismoidal rule.

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Chapter 5 Solutions