Explanation Formula used: Trapezoidal rule: Let f be a function on an interval [ a , b ] . Partition [ a , b ] into n subintervals of equal length Δ x = ( b − a ) / n with end points a = x 0 < x 1 < x 2 < ... < x n = b . Then T n = [ f ( x 0 ) + 2 f ( x 1 ) + 2 f ( x 2 ) + .... + 2 f ( x n − 1 ) + f ( x n ) ] Δ x / 2 is an approximation of ∫ a b f ( x ) d x . Calculation: The given interval is [ a , b ] = [ 2 , 4 ] and number of partitions n = 5 . Divide the interval [ 2 , 4 ] into five equal subintervals. So, the length of each subinterval becomes, Δ x = ( b − a ) / n = ( 4 − 2 ) / 5 = 2 / 5 = 0.4 Thus, the length of each interval is 0.4. So, the end points of the each subinterval are x 0 = 2 , x 1 = 2.4 , x 2 = 2.8 , x 3 = 3.2 , x 4 = 3.6 and x 5 = 4 . Calculate the value of the function f ( x ) = 81 + x 5 at each end point as follows. x f ( x ) 2.0 81 + x 5 = 81 + ( 2 ) 5 = 10

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

13th Edition

ISBN: 9780321945518

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Publisher: PEARSON

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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 14.4, Problem 1MP

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To find: The approximate value of the integral ∫2481+x5dx using the trapezoidal rule.

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Chapter 14.3, Problem 83E

Chapter 14.4, Problem 2MP

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Chapter 14 Solutions

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

Ch. 14.1 - Prob. 1MP Ch. 14.1 - Prob. 2MP Ch. 14.1 - Prob. 3MP Ch. 14.1 - Prob. 4MP Ch. 14.1 - Matched Problem 5 Find the area bounded by...Ch. 14.1 - Prob. 6MP Ch. 14.1 - Prob. 7MP Ch. 14.1 - Prob. 1ED Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E

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The approximate value of the integral ∫ 2 4 81 + x 5 d x using the trapezoidal rule.

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To find: The approximate value of the integral ∫2481+x5dx using the trapezoidal rule.

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Chapter 14 Solutions