Explanation Given: The interval is [ 0 , 12 ] and the corresponding interval is partition into four subintervals. 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 [ 0 , 12 ] into 4 subintervals, the equal length is calculated as follows. Δ x = 12 − 0 4 = 12 4 = 3 By the help of the equal length, the endpoints becomes a = 0 < 3 < 6 < 9 < 12 = b . Since the value c n = x n − 1 + 2 x n 3 , the values of c 1 , c 2 , c 3 , and c 4 are 2 , 5 , 8 and 11 . Calculate the value of f ( x ) = 25 − 3 x 2 at c 1 = 2 . f ( 1 ) = 25 − 3 ( 2 ) 2 = 25 − 12 = 13 Calculate the value of f ( x ) = 25 − 3 x 2 at c 2 = 5

COLL.MATH F/BUS ECO.(LL+18 WEEK MYLAB E)

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ISBN: 9780135998083

Author: Barnett

Publisher: PEARSON

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Chapter 12.4, Problem 24E

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To calculate: The Riemann sum of the function f(x)=25−3x2 on the interval [0,12].

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Chapter 12.4, Problem 23E

Chapter 12.4, Problem 25E

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COLL.MATH F/BUS ECO.(LL+18 WEEK MYLAB E)

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The Riemann sum of the function f ( x ) = 25 − 3 x 2 on the interval [ 0 , 12 ] .

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To calculate: The Riemann sum of the function f(x)=25−3x2 on the interval [0,12].

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Chapter 12 Solutions