Explanation Given: a) ∫ 0 18 A ( h ) d h b) n = 9 (10 data `s are given which is equally spaced of width size 2 ) c) Trapezoidal rule approximation. d) a = 0 and b = 18 h ( f t ) A ( h ) (acres) 0 2.8 2 2.4 4 1.8 6 1.5 8 1.2 10 0.8 12 0.6 14 0.2 16 0.1 18 0 Formula Used: The Trapezoidal rule approximation is: ∫ a b f ( h ) d h ≈ H 2 × [ f ( h 0 ) + 2 f ( h 1 ) + 2 f ( h 2 ) + ...2 f ( h n − 1 ) + f ( h n ) ] Where, n + 1 Data are equally spaced. H = Width of interval. n = No. of intervals. H = b − a n h 0 = a h n = a + n H Calculation: Volume of the pond given by = ∫ a b A ( h ) d h Where, f ( h ) = A ( h ) a = 0 and b = 18 H = Width of interval ∴ H = b − a n H = 18 − 0 9 H = 2 So end points are which is given below in the table, h n = a + n H h ( f t ) A ( h ) (acres) h 0 0 2.8 h 1 2 2.4 h 2 4 1.8 h 3 6 1.5 h 4 8 1.2 h 5 10 0.8 h 6 12 0.6 h 7 14 0.2 h 8 16 0.1 h 9 18 0 Now evaluating the value of function at the end points: ∵ f ( h ) = A ( h ) f ( h 0 ) = A ( h 0 ) = 2...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 8, Problem 105CRE

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Chapter 8, Problem 104CRE

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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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Volume of the pond.

Solution Summary: The author explains the Trapezoidal rule approximation to determine the volume of the pond.

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