Explanation Given: Consider the cross-sectional areas given in the text book, these are measured at 2-meter intervals along the length of an irregularly shaped object. x 0 1 2 3 4 5 6 7 8 9 10 A 1.12 1.09 1.05 1.03 0.99 1.01 0.98 0.99 0.96 0.93 0.91 Formula Used: A solid S with known cross-sectional area A(x), perpendicular to the x-axis at each point on the interval [ a , b ] has volume V = ∫ a b A ( x ) d x Calculation: Use the Simpson’s rule for a domain divided into N equally spaced sub-intervals, ∫ a b f ( x ) d x = b − a 3 N [ f ( x 0 ) + 4 f ( x 1 ) + 2 f ( x 2 ) + 4 f ( x 3 ) + ... + 4 f ( x N − 1 ) + f ( x N ) ] Here, a = x 0 < x 1 < x 2 < x 3 < ... < x N − 1 < x N = b The cross-sectional areas of the given object are given from x = 0 and x = 20

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Chapter 6.2, Problem 55PS

To determine

To estimate:The volume of an irregular shaped object.

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Chapter 6.2, Problem 54PS

Chapter 6.2, Problem 56PS

Chapter 6 Solutions

Calculus

Ch. 6.1 - Prob. 1PS Ch. 6.1 - Prob. 2PS Ch. 6.1 - Prob. 3PS Ch. 6.1 - Prob. 4PS Ch. 6.1 - Prob. 5PS Ch. 6.1 - Prob. 6PS Ch. 6.1 - Prob. 7PS Ch. 6.1 - Prob. 8PS Ch. 6.1 - Prob. 9PS Ch. 6.1 - Prob. 10PS

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To estimate: The volume of an irregular shaped object.

Solution Summary: The author calculates the volume of an irregular shaped object by using the Simpson's rule for a domain divided into N equally spaced sub-intervals.

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To estimate:The volume of an irregular shaped object.

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Chapter 6 Solutions