Explanation Given: f ( x ) = ( 1 + x 2 ) − 1 on interval [ 0 , 1 ] with subinterval n=5 Formula: ∫ a b f ( x ) d x = △ x ( f ( x 1 ) + f ( x 2 ) + .......... + f ( x n ) ) Where, △ x = b − a n Calculation: For R 5 , It is right end sum for each interval and rectangle. a = 0 , b = 1 and n = 5 Therefore, △ x = 1 − 0 5 Divide the interval [ 0 , 1 ] into n = 5 subinterval of length △ x = 1 5 x 1 = 1 5 , x 2 = 2 5 , x 3 = 3 5 , x 4 = 4 5 , x 5 = 1 f ( x 1 ) = f ( 1 5 ) = 25 26 = 0.961538461538462 f ( x 2 ) = f ( 2 5 ) = 25 29 = 0.862068965517241 f ( x 3 ) = f ( 3 5 ) = 25 34 = 0.735294117647059 f ( x 4 ) = f ( 4 5 ) = 25 41 = 0.609756097560976 f ( x 5 ) = f ( 1 ) = 1 2 = 0.5 Now, set up the above values into formula R 5 = 1 5 ( 0.961538 + 0.862068 + 0.735294 + 0.609756 + 0.5 ) R 5 = 0.733731 For M 6 , It is mid point of each rectangle. a = 0 , b = 1 and n = 5 Therefore, △ x = 1 − 0 5 Divide the interval [ 0 , 1 ] into n = 5 subinterval of length △ x = 1 5 f ( x 0 + x 1 2 ) = f ( ( 0 ) + ( 1 5 ) 2 ) = f ( 1 10 ) = 100 101 = 0.990099 f ( x 1 + x 2 2 ) = f ( ( 1 5 ) + ( 2 5 ) 2 ) = f ( 3 10 ) = 100 109 = 0...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 5, Problem 9CRE

To determine

$R_{5}, M_{5}$ and $L_{5}$ using Riemann sum formula

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Chapter 5, Problem 8CRE

Chapter 5, Problem 10CRE

Chapter 5 Solutions

CALCULUS (CLOTH)

Ch. 5.1 - Prob. 1PQ Ch. 5.1 - Prob. 2PQ Ch. 5.1 - Prob. 3PQ Ch. 5.1 - Prob. 4PQ Ch. 5.1 - Prob. 5PQ Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E

Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - 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