Explanation Given: The given integral is ∫ 0 1 x 2 d x . Concept used: If f and g are integrable on [ a , b ] , and f ( x ) ≤ g ( x ) throughout the interval then by Dominance rule of definite integral ∫ a b f ( x ) d x ≤ ∫ a b g ( x ) d x Formula Used: Formula to evaluate the integral of the form ∫ a x n d x is shown below. ∫ a x n d x = a ∫ x n d x = a x n + 1 n + 1 + C , n ≠ − 1 Fundamental theorem of Calculus I: ∫ a b f ( x ) d x = F ( b ) − F ( a ) Where F ′ ( x ) = f ( x ) Calculation: Consider the integral ∫ 0 1 x 2 d x

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 5.3, Problem 39PS

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To establish: The inequality ∫01x2dx≤12 .

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Chapter 5.3, Problem 38PS

Chapter 5.3, Problem 40PS

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Chapter 5 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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To establish: The inequality ∫ 0 1 x 2 d x ≤ 1 2 .

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To establish: The inequality ∫01x2dx≤12 .

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Chapter 5 Solutions