Explanation Given info. F is increasing and concave up on [ a , b ] . F is increasing and concave down in second consideration. Formula used: ∫ a b f ( x ) . d x ≃ ∑ i = 1 n f ( x i − 1 ) . Δ x = L N ∫ a b f ( x ) . d x ≃ ∑ i = 1 n f ( x i ) . Δ x = R N Proof: f ( x ) is increasing and concave up on [ a , b ] . From the above graph it becomes clear that if you take left approximation. ∫ a b f ( x ) . d x ≃ ∑ i = 1 n f ( x i − 1 ) . Δ x = L N ∫ a b f ( x ) . d x = L N + ( Sum oof area of triangles formed below the graph ) ⋯ ⋯ ( 1 ) You take Right approximation ∫ a b f ( x ) . d x ≃ ∑ i = 1 n f ( x i ) . Δ x = R N ∫ a b f ( x ) . d x = R N − ( Sum of area of triangles formed above the graph ) ⋯ ⋯ ( 2 ) If f is increasing and concave down, then From this figure it becomes clear that (Area of triangle formed above the graph) So (Sum of all area of triangles formed above the graph) × (Area of triangles formed below the graph) When you use left end approximation the, ∫ a b f ( s ) ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 5, Problem 92CRE

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To proof:

If f is increasing a con cave up on $[a, b]$ . Then $L_{N}$ is more accurate than $R_{N}$ . Also decide that which is more accurate if f is increasing and concave down?

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Chapter 5, Problem 91CRE

Chapter 5, Problem 93CRE

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Chapter 5 Solutions

Calculus - Standalone book

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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Prob. 21E Ch. 5.5 - Prob. 22E Ch. 5.5 - Prob. 23E Ch. 5.5 - Prob. 24E Ch. 5.5 - Prob. 25E Ch. 5.5 - Prob. 26E Ch. 5.5 - Prob. 27E Ch. 5.5 - Prob. 28E Ch. 5.5 - Prob. 29E Ch. 5.5 - Prob. 30E Ch. 5.5 - Prob. 31E Ch. 5.5 - Prob. 32E Ch. 5.5 - Prob. 33E Ch. 5.5 - Prob. 34E Ch. 5.5 - Prob. 35E Ch. 5.5 - Prob. 36E Ch. 5.5 - Prob. 37E Ch. 5.5 - Prob. 38E Ch. 5.5 - Prob. 39E Ch. 5.5 - Prob. 40E Ch. 5.5 - Prob. 41E Ch. 5.5 - Prob. 42E Ch. 5.5 - Prob. 43E Ch. 5.5 - Prob. 44E Ch. 5.5 - Prob. 45E Ch. 5.5 - Prob. 46E Ch. 5.5 - Prob. 47E Ch. 5.5 - Prob. 48E Ch. 5.5 - Prob. 49E Ch. 5.5 - Prob. 50E Ch. 5.5 - Prob. 51E Ch. 5.5 - Prob. 52E Ch. 5.5 - Prob. 53E Ch. 5.6 - Prob. 1PQ Ch. 5.6 - Prob. 2PQ Ch. 5.6 - Prob. 3PQ Ch. 5.6 - Prob. 1E Ch. 5.6 - Prob. 2E Ch. 5.6 - Prob. 3E Ch. 5.6 - Prob. 4E Ch. 5.6 - Prob. 5E Ch. 5.6 - Prob. 6E Ch. 5.6 - Prob. 7E Ch. 5.6 - Prob. 8E Ch. 5.6 - Prob. 9E Ch. 5.6 - Prob. 10E Ch. 5.6 - Prob. 11E Ch. 5.6 - Prob. 12E Ch. 5.6 - Prob. 13E Ch. 5.6 - Prob. 14E Ch. 5.6 - Prob. 15E Ch. 5.6 - Prob. 16E Ch. 5.6 - Prob. 17E Ch. 5.6 - Prob. 18E Ch. 5.6 - Prob. 19E Ch. 5.6 - Prob. 20E Ch. 5.6 - Prob. 21E Ch. 5.6 - Prob. 22E Ch. 5.6 - Prob. 23E Ch. 5.6 - Prob. 24E Ch. 5.6 - Prob. 25E Ch. 5.6 - Prob. 26E Ch. 5.6 - Prob. 27E Ch. 5.6 - Prob. 28E Ch. 5.6 - Prob. 29E Ch. 5.6 - Prob. 30E Ch. 5.6 - Prob. 31E Ch. 5.7 - Prob. 1PQ Ch. 5.7 - Prob. 2PQ Ch. 5.7 - Prob. 3PQ Ch. 5.7 - Prob. 1E Ch. 5.7 - Prob. 2E Ch. 5.7 - Prob. 3E Ch. 5.7 - Prob. 4E Ch. 5.7 - Prob. 5E Ch. 5.7 - Prob. 6E Ch. 5.7 - Prob. 7E Ch. 5.7 - Prob. 8E Ch. 5.7 - Prob. 9E Ch. 5.7 - Prob. 10E Ch. 5.7 - Prob. 11E Ch. 5.7 - Prob. 12E Ch. 5.7 - Prob. 13E Ch. 5.7 - Prob. 14E Ch. 5.7 - Prob. 15E Ch. 5.7 - Prob. 16E Ch. 5.7 - Prob. 17E Ch. 5.7 - Prob. 18E Ch. 5.7 - Prob. 19E Ch. 5.7 - Prob. 20E Ch. 5.7 - Prob. 21E Ch. 5.7 - Prob. 22E Ch. 5.7 - Prob. 23E Ch. 5.7 - Prob. 24E Ch. 5.7 - Prob. 25E Ch. 5.7 - Prob. 26E Ch. 5.7 - Prob. 27E Ch. 5.7 - Prob. 28E Ch. 5.7 - Prob. 29E Ch. 5.7 - Prob. 30E Ch. 5.7 - Prob. 31E Ch. 5.7 - Prob. 32E Ch. 5.7 - Prob. 33E Ch. 5.7 - Prob. 34E Ch. 5.7 - Prob. 35E Ch. 5.7 - Prob. 36E Ch. 5.7 - Prob. 37E Ch. 5.7 - Prob. 38E Ch. 5.7 - Prob. 39E Ch. 5.7 - Prob. 40E Ch. 5.7 - Prob. 41E Ch. 5.7 - Prob. 42E Ch. 5.7 - Prob. 43E Ch. 5.7 - Prob. 44E Ch. 5.7 - Prob. 45E Ch. 5.7 - Prob. 46E Ch. 5.7 - Prob. 47E Ch. 5.7 - Prob. 48E Ch. 5.7 - Prob. 49E Ch. 5.7 - Prob. 50E Ch. 5.7 - Prob. 51E Ch. 5.7 - Prob. 52E Ch. 5.7 - Prob. 53E Ch. 5.7 - Prob. 54E Ch. 5.7 - Prob. 55E Ch. 5.7 - Prob. 56E Ch. 5.7 - Prob. 57E Ch. 5.7 - Prob. 58E Ch. 5.7 - Prob. 59E Ch. 5.7 - Prob. 60E Ch. 5.7 - Prob. 61E Ch. 5.7 - Prob. 62E Ch. 5.7 - Prob. 63E Ch. 5.7 - Prob. 64E Ch. 5.7 - Prob. 65E Ch. 5.7 - Prob. 66E Ch. 5.7 - Prob. 67E Ch. 5.7 - Prob. 68E Ch. 5.7 - Prob. 69E Ch. 5.7 - Prob. 70E Ch. 5.7 - Prob. 71E Ch. 5.7 - Prob. 72E Ch. 5.7 - Prob. 73E Ch. 5.7 - Prob. 74E Ch. 5.7 - Prob. 75E Ch. 5.7 - Prob. 76E Ch. 5.7 - Prob. 77E Ch. 5.7 - Prob. 78E Ch. 5.7 - Prob. 79E Ch. 5.7 - Prob. 80E Ch. 5.7 - Prob. 81E Ch. 5.7 - Prob. 82E Ch. 5.7 - 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To proof: If f is increasing a con cave up on [ a , b ] . Then L N is more accurate than R N . Also decide that which is more accurate if f is increasing and concave down?

Solution Summary: The author explains that if f is increasing and concave up on [a, b] then L N is more accurate than R N.

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To proof:

If f is increasing a con cave up on $[a, b]$ . Then $L_{N}$ is more accurate than $R_{N}$ . Also decide that which is more accurate if f is increasing and concave down?

Want to see the full answer?

Chapter 5 Solutions

To proof: If f is increasing a con cave up on [ a , b ] . Then L N is more accurate than R N . Also decide that which is more accurate if f is increasing and concave down?

Solution Summary: The author explains that if f is increasing and concave up on [a, b] then L N is more accurate than R N.

Concept explainers

Videos

To proof: If f is increasing a con cave up on [a,b]. Then LNis more accurate than RN. Also decide that which is more accurate if f is increasing and concave down?

Want to see the full answer?

Chapter 5 Solutions

To proof:

If f is increasing a con cave up on $[a, b]$ . Then $L_{N}$ is more accurate than $R_{N}$ . Also decide that which is more accurate if f is increasing and concave down?