Explanation Given information: Consider f ( x ) = 9 − x 2 on [0,3], n = 3 . Formula used: Let f is continuous function defined on an interval [ a , b ] , n is a positive integer. Δ x = b − a n , x k = a + k Δ x . The midpoint Riemann sum is given by M R S = ∑ k = 1 n f ( x k * ) Δ x Calculation: Find the midpoint sum Δ x = b − a n = 3 − 0 3 = 1 x k = a + k Δ x = 0 + k ( 1 ) = k ⇒ x k − 1 = k − 1 x k * = x k − 1 + x k 2 = k − 1 + k 2 = k − 0

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Question

Chapter 4, Problem 9SC

To determine

To find: The midpoint Riemann sum of the given definite integral f on [a,b].

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Chapter 4, Problem 8SC

Chapter 4, Problem 10SC

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Chapter 4 Solutions

Calculus

Ch. 4.1 - Prob. 1TB Ch. 4.1 - Prob. 2TB Ch. 4.1 - Prob. 3TB Ch. 4.1 - Prob. 0C Ch. 4.1 - Prob. 1C Ch. 4.1 - Prob. 2C Ch. 4.1 - Prob. 3C Ch. 4.1 - Prob. 4C Ch. 4.1 - Prob. 5C Ch. 4.1 - Prob. 6C

Ch. 4.1 - Prob. 7C Ch. 4.1 - Prob. 8C Ch. 4.1 - Prob. 9C Ch. 4.1 - Prob. 10C Ch. 4.1 - Prob. 11C Ch. 4.1 - Prob. 12C Ch. 4.1 - Prob. 13C Ch. 4.1 - Prob. 14C Ch. 4.1 - Prob. 15C Ch. 4.1 - Prob. 16C Ch. 4.1 - Prob. 17C Ch. 4.1 - Prob. 18C Ch. 4.1 - Prob. 19C Ch. 4.1 - Prob. 20C Ch. 4.1 - Prob. 21S Ch. 4.1 - Prob. 22S Ch. 4.1 - Prob. 23S Ch. 4.1 - Prob. 24S Ch. 4.1 - Prob. 25S Ch. 4.1 - Prob. 26S Ch. 4.1 - Prob. 27S Ch. 4.1 - Prob. 28S Ch. 4.1 - Prob. 29S Ch. 4.1 - Prob. 30S Ch. 4.1 - Prob. 31S Ch. 4.1 - Prob. 32S Ch. 4.1 - Prob. 33S Ch. 4.1 - Prob. 34S Ch. 4.1 - Prob. 35S Ch. 4.1 - Prob. 36S Ch. 4.1 - Prob. 37S Ch. 4.1 - Prob. 38S Ch. 4.1 - Prob. 39S Ch. 4.1 - Prob. 40S Ch. 4.1 - Prob. 41S Ch. 4.1 - Prob. 42S Ch. 4.1 - Prob. 43S Ch. 4.1 - Prob. 44S Ch. 4.1 - Prob. 45S Ch. 4.1 - Prob. 46S Ch. 4.1 - Prob. 47S Ch. 4.1 - Prob. 48S Ch. 4.1 - Prob. 49S Ch. 4.1 - Prob. 50S Ch. 4.1 - Prob. 51S Ch. 4.1 - Prob. 52S Ch. 4.1 - Prob. 53A Ch. 4.1 - Prob. 54A Ch. 4.1 - Prob. 55A Ch. 4.1 - Prob. 56A Ch. 4.1 - 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Prob. 59S Ch. 4.5 - Prob. 60S Ch. 4.5 - Prob. 61S Ch. 4.5 - Prob. 62S Ch. 4.5 - Prob. 63S Ch. 4.5 - Prob. 64S Ch. 4.5 - Prob. 65A Ch. 4.5 - Prob. 66A Ch. 4.5 - Prob. 67A Ch. 4.5 - Prob. 68A Ch. 4.5 - Prob. 69A Ch. 4.5 - Prob. 70A Ch. 4.5 - Prob. 71A Ch. 4.5 - Prob. 72P Ch. 4.5 - Prob. 73P Ch. 4.5 - Prob. 74P Ch. 4.5 - Prob. 75P Ch. 4.5 - Prob. 76P Ch. 4.5 - Prob. 77P Ch. 4.5 - Prob. 78P Ch. 4.5 - Prob. 79P Ch. 4.5 - Prob. 80P Ch. 4.5 - Prob. 1TF Ch. 4.5 - Prob. 2TF Ch. 4.5 - Prob. 3TF Ch. 4.5 - Prob. 4TF Ch. 4.5 - Prob. 5TF Ch. 4.5 - Prob. 6TF Ch. 4.6 - Prob. 1TB Ch. 4.6 - Prob. 2TB Ch. 4.6 - Prob. 3TB Ch. 4.6 - Prob. 4TB Ch. 4.6 - Prob. 5TB Ch. 4.6 - Prob. 0C Ch. 4.6 - Prob. 1C Ch. 4.6 - Prob. 2C Ch. 4.6 - Prob. 3C Ch. 4.6 - Prob. 4C Ch. 4.6 - Prob. 5C Ch. 4.6 - Prob. 6C Ch. 4.6 - Prob. 7C Ch. 4.6 - Prob. 8C Ch. 4.6 - Prob. 9C Ch. 4.6 - Prob. 10C Ch. 4.6 - Prob. 11C Ch. 4.6 - Prob. 12C Ch. 4.6 - Prob. 13C Ch. 4.6 - Prob. 14C Ch. 4.6 - Prob. 15C Ch. 4.6 - Prob. 16C Ch. 4.6 - Prob. 17C Ch. 4.6 - Prob. 18C Ch. 4.6 - Prob. 19C Ch. 4.6 - Prob. 20C Ch. 4.6 - Prob. 21C Ch. 4.6 - Prob. 22C Ch. 4.6 - Prob. 23S Ch. 4.6 - Prob. 24S Ch. 4.6 - Prob. 25S Ch. 4.6 - Prob. 26S Ch. 4.6 - Prob. 27S Ch. 4.6 - Prob. 28S Ch. 4.6 - Prob. 29S Ch. 4.6 - Prob. 30S Ch. 4.6 - Prob. 31S Ch. 4.6 - Prob. 32S Ch. 4.6 - Prob. 33S Ch. 4.6 - Prob. 34S Ch. 4.6 - Prob. 35S Ch. 4.6 - Prob. 36S Ch. 4.6 - Prob. 37S Ch. 4.6 - Prob. 38S Ch. 4.6 - Prob. 39S Ch. 4.6 - Prob. 40S Ch. 4.6 - Prob. 41S Ch. 4.6 - Prob. 42S Ch. 4.6 - Prob. 43S Ch. 4.6 - Prob. 44S Ch. 4.6 - Prob. 45S Ch. 4.6 - Prob. 46S Ch. 4.6 - Prob. 47S Ch. 4.6 - Prob. 48S Ch. 4.6 - Prob. 49S Ch. 4.6 - Prob. 50S Ch. 4.6 - Prob. 51S Ch. 4.6 - Prob. 52S Ch. 4.6 - Prob. 53S Ch. 4.6 - Prob. 54S Ch. 4.6 - Prob. 55S Ch. 4.6 - Prob. 56S Ch. 4.6 - Prob. 57S Ch. 4.6 - Prob. 58S Ch. 4.6 - Prob. 59S Ch. 4.6 - Prob. 60S Ch. 4.6 - Prob. 61S Ch. 4.6 - Prob. 62S Ch. 4.6 - Prob. 63S Ch. 4.6 - Prob. 64S Ch. 4.6 - Prob. 65S Ch. 4.6 - Prob. 66S Ch. 4.6 - Prob. 67S Ch. 4.6 - Prob. 68S Ch. 4.6 - Prob. 69S Ch. 4.6 - Prob. 70S Ch. 4.6 - Prob. 71S Ch. 4.6 - Prob. 72S Ch. 4.6 - Prob. 73S Ch. 4.6 - Prob. 74A Ch. 4.6 - Prob. 75A Ch. 4.6 - Prob. 76A Ch. 4.6 - Prob. 77A Ch. 4.6 - Prob. 78P Ch. 4.6 - Prob. 79P Ch. 4.6 - Prob. 80P Ch. 4.6 - Prob. 81P Ch. 4.6 - Prob. 82P Ch. 4.6 - Prob. 1TF Ch. 4.6 - Prob. 2TF Ch. 4.6 - Prob. 3TF Ch. 4.6 - Prob. 4TF Ch. 4.6 - Prob. 5TF Ch. 4.7 - Prob. 1TB Ch. 4.7 - Prob. 2TB Ch. 4.7 - Prob. 3TB Ch. 4.7 - Prob. 0C Ch. 4.7 - Prob. 1C Ch. 4.7 - Prob. 2C Ch. 4.7 - Prob. 3C Ch. 4.7 - Prob. 4C Ch. 4.7 - Prob. 5C Ch. 4.7 - Prob. 6C Ch. 4.7 - Prob. 7C Ch. 4.7 - Prob. 8C Ch. 4.7 - Prob. 9C Ch. 4.7 - Prob. 10C Ch. 4.7 - Prob. 11C Ch. 4.7 - Prob. 12C Ch. 4.7 - Prob. 13C Ch. 4.7 - Prob. 14C Ch. 4.7 - Prob. 15C Ch. 4.7 - Prob. 16C Ch. 4.7 - Prob. 17C Ch. 4.7 - Prob. 18C Ch. 4.7 - Prob. 19C Ch. 4.7 - Prob. 20C Ch. 4.7 - Prob. 21C Ch. 4.7 - Prob. 22C Ch. 4.7 - Prob. 23C Ch. 4.7 - Prob. 24C Ch. 4.7 - Prob. 25C Ch. 4.7 - Prob. 26C Ch. 4.7 - Prob. 27S Ch. 4.7 - Prob. 28S Ch. 4.7 - Prob. 29S Ch. 4.7 - Prob. 30S Ch. 4.7 - Prob. 31S Ch. 4.7 - Prob. 32S Ch. 4.7 - Prob. 33S Ch. 4.7 - Prob. 34S Ch. 4.7 - Prob. 35S Ch. 4.7 - Prob. 36S Ch. 4.7 - Prob. 37S Ch. 4.7 - Prob. 38S Ch. 4.7 - Prob. 39S Ch. 4.7 - Prob. 40S Ch. 4.7 - Prob. 41S Ch. 4.7 - Prob. 42S Ch. 4.7 - Prob. 43S Ch. 4.7 - Prob. 44S Ch. 4.7 - Prob. 45S Ch. 4.7 - Prob. 46S Ch. 4.7 - Prob. 47S Ch. 4.7 - Prob. 48S Ch. 4.7 - Prob. 49S Ch. 4.7 - Prob. 50S Ch. 4.7 - Prob. 51S Ch. 4.7 - Prob. 52S Ch. 4.7 - Prob. 53S Ch. 4.7 - Prob. 54S Ch. 4.7 - Prob. 55S Ch. 4.7 - Prob. 56S Ch. 4.7 - Prob. 57S Ch. 4.7 - Prob. 58S Ch. 4.7 - Prob. 59A Ch. 4.7 - Prob. 60A Ch. 4.7 - Prob. 61A Ch. 4.7 - Prob. 62A Ch. 4.7 - Prob. 63P Ch. 4.7 - Prob. 64P Ch. 4.7 - Prob. 65P Ch. 4.7 - Prob. 66P Ch. 4.7 - Prob. 67P Ch. 4.7 - Prob. 68P Ch. 4.7 - Prob. 69P Ch. 4.7 - Prob. 70P Ch. 4.7 - Prob. 71P Ch. 4.7 - Prob. 72P Ch. 4.7 - Prob. 73P Ch. 4.7 - Prob. 74P Ch. 4.7 - Prob. 75P Ch. 4.7 - Prob. 76P Ch. 4.7 - Prob. 77P Ch. 4.7 - Prob. 78P Ch. 4.7 - Prob. 1TF Ch. 4.7 - Prob. 2TF Ch. 4.7 - Prob. 3TF Ch. 4.7 - Prob. 4TF Ch. 4.7 - Prob. 5TF Ch. 4.7 - Prob. 6TF Ch. 4.7 - Prob. 7TF Ch. 4.7 - Prob. 8TF Ch. 4 - Prob. 1D Ch. 4 - Prob. 2D Ch. 4 - Prob. 3D Ch. 4 - Prob. 4D Ch. 4 - Prob. 5D Ch. 4 - Prob. 6D Ch. 4 - Prob. 7D Ch. 4 - Prob. 8D Ch. 4 - Prob. 9D Ch. 4 - Prob. 10D Ch. 4 - Prob. 11D Ch. 4 - Prob. 12D Ch. 4 - Prob. 13D Ch. 4 - Prob. 1T Ch. 4 - Prob. 2T Ch. 4 - Prob. 3T Ch. 4 - Prob. 4T Ch. 4 - Prob. 5T Ch. 4 - Prob. 6T Ch. 4 - Prob. 7T Ch. 4 - Prob. 8T Ch. 4 - Prob. 9T Ch. 4 - Prob. 10T Ch. 4 - Prob. 11T Ch. 4 - Prob. 12T Ch. 4 - Prob. 13T Ch. 4 - Prob. 1NFAR Ch. 4 - Prob. 2NFAR Ch. 4 - Prob. 3NFAR Ch. 4 - Prob. 4NFAR Ch. 4 - Prob. 5NFAR Ch. 4 - Prob. 6NFAR Ch. 4 - Prob. 7NFAR Ch. 4 - Prob. 8NFAR Ch. 4 - Prob. 9NFAR Ch. 4 - Prob. 10NFAR Ch. 4 - Prob. 11NFAR Ch. 4 - Prob. 12NFAR Ch. 4 - Prob. 13NFAR Ch. 4 - Prob. 14NFAR Ch. 4 - Prob. 15NFAR Ch. 4 - Prob. 16NFAR Ch. 4 - Prob. 17NFAR Ch. 4 - Prob. 18NFAR Ch. 4 - Prob. 19NFAR Ch. 4 - 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Prob. 16SC Ch. 4 - Prob. 17SC Ch. 4 - Prob. 18SC Ch. 4 - Prob. 19SC Ch. 4 - Prob. 20SC Ch. 4 - Prob. 21SC Ch. 4 - Prob. 22SC Ch. 4 - Prob. 23SC Ch. 4 - Prob. 24SC Ch. 4 - Prob. 25SC Ch. 4 - Prob. 26SC Ch. 4 - Prob. 27SC Ch. 4 - Prob. 28SC Ch. 4 - Prob. 29SC Ch. 4 - Prob. 30SC Ch. 4 - Prob. 31SC Ch. 4 - Prob. 32SC Ch. 4 - Prob. 33SC Ch. 4 - Prob. 34SC Ch. 4 - Prob. 35SC Ch. 4 - Prob. 36SC Ch. 4 - Prob. 37SC Ch. 4 - Prob. 38SC Ch. 4 - Prob. 39SC Ch. 4 - Prob. 40SC Ch. 4 - Prob. 41SC Ch. 4 - Prob. 42SC Ch. 4 - Prob. 43SC Ch. 4 - Prob. 44SC Ch. 4 - Prob. 45SC Ch. 4 - Prob. 46SC Ch. 4 - Prob. ACP Ch. 4 - Prob. BCP Ch. 4 - Prob. CCP Ch. 4 - Prob. DCP

Knowledge Booster

The midpoint Riemann sum of the given definite integral f on [ a , b ] .

Solution Summary: The author calculates the midpoint Riemann sum of the given definite integral f on [a,b].

To find: The midpoint Riemann sum of the given definite integral f on [a,b].

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Chapter 4 Solutions