Explanation Given: The interval is [ − 5 , 5 ] and the corresponding interval is partition into five subintervals. The value of c 1 , c 2 , c 3 , c 4 and c 5 are − 4 , − 1 , 1 , 2 and 5 , respectively. Formula used: “Let f be a function defined on the interval [ a , b ] and partition the interval into n subintervals of equal length Δ x = b − a n with endpoints a = x 0 < x 1 < x 2 < … < x n = b . Then, Riemann sum is defined: S n = f ( c 1 ) Δ x + f ( c 2 ) Δ x + … + f ( c n ) Δ x , where c n ∈ [ x n − 1 , x n ] .” Calculation: Divide the interval [ − 5 , 5 ] into 5 subintervals, the equal length is calculated as follows. Δ x = 5 + 5 5 = 10 5 = 2 Calculate the value of f ( x ) = 100 − x 2 at c 1 = − 4 . f ( − 4 ) = 100 − ( − 4 ) 2 = 100 − 16 = 84 Calculate the value of f ( x ) = 100 − x 2 at c 2 = − 1

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

14th Edition

ISBN: 9780134674148

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

Publisher: PEARSON

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Chapter 12, Problem 23RE

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To calculate: The Riemann sum of the function f(x)=100−x2 on the interval [−5,5].

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Chapter 12, Problem 22RE

Chapter 12, Problem 24RE

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Chapter 12 Solutions

College Mathematics for Business, Economics, Life Sciences, and Social Sciences (14th Edition)

Ch. 12.1 - Matched Problem 1 Note that Find all...Ch. 12.1 - Prob. 2MP Ch. 12.1 - Prob. 3MP Ch. 12.1 - Prob. 4MP Ch. 12.1 - Prob. 5MP Ch. 12.1 - Prob. 6MP Ch. 12.1 - Prob. 1ED Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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The Riemann sum of the function f ( x ) = 100 − x 2 on the interval [ − 5 , 5 ] .

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To calculate: The Riemann sum of the function f(x)=100−x2 on the interval [−5,5].

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Chapter 12 Solutions