Explanation Given information: Given, F ' ( x ) = 2 x 2 + 5 and F ( 0 ) = 3 . b = 0, 0.1, 0.2, 0.5, and 1.0. Calculation: According to the Fundamental Theorem ∫ a b F ' ( t ) d t = F ( b ) − F ( a ) Using the above rule, F ( b ) − F ( 0 ) = ∫ 0 b F ' ( x ) d X F ( b ) = ∫ 0 b F ' ( x ) d x + F ( 0 ) F ( b ) = ∫ 0 b ( 2 x 2 + 5 ) d x + F ( 0 ) F ( b ) = [ 2 x 3 3 + 5 x ] 0 b + F ( 0 ) F ( b ) = [ ( 2 b 3 3 + 5 b ) − ( 2 ( 0 ) 3 3 + 5 ( 0 ) ) ] + 3 F ( b ) = [ ( 2 b 3 3 + 5 b ) − ( 0 + 0 ) ] + 3 F ( b ) = 2 b 3 3 + 5 b + 3 Plugging b = 0, F ( b ) = 2 b 3 3 + 5 b + 3 F ( 0 ) = 2 ( 0 ) 3 3 + 5 ( 0 ) + 3 F ( 0 ) = 2 ( 0 ) 3 + 0 + 3 F ( 0 ) = 3 Plugging b = 0.1, F ( b ) = 2 b 3 3 + 5 b + 3 F ( 0.1 ) = 2 ( 0.1 ) 3 3 + 5 ( 0.1 ) + 3 F ( 0.1 ) = 2 ( 0.001 ) 3 + 0.5 + 3 F ( 0.1 ) = 0.002 3 + 0.5 + 3 F ( 0.1 ) = 0.002 3 + 1.5 3 + 9 3 F ( 0.1 ) = 0.002 + 1.5 + 9 3 F ( 0.1 ) = 10.502 3 F ( 0

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 6.1, Problem 1P

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To find the value of F ( b ) for b = 0, 0.1, 0.2, 0.5, and 1.0.

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Chapter 5, Problem 11FOT

Chapter 6.1, Problem 2P

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To find the value of F ( b ) for b = 0, 0.1, 0.2, 0.5, and 1.0.

Solution Summary: The author calculates the value of F (b) for b = 0, 0, 0.2, 0.5, and 1.0 based on the Fundamental Theorem.

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To find the value of F ( b ) for b = 0, 0.1, 0.2, 0.5, and 1.0.

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Chapter 6 Solutions