Explanation Given information: The given function is f ( x ) = x 2 cos 3 x . Formula used: 1) The general power rule of integration , ∫ f n ( x ) d x = f n + 1 ( x ) n + 1 ⋅ 1 f ′ ( x ) + C Where C is the constant of integration. 2) Integration by parts: ∫ f ( x ) g ( x ) d x = f ( x ) G ( x ) − ∫ f ′ ( x ) G ( x ) d x Where f ' ( x ) is derivative of f ( x ) and G ( x ) is an anti-derivative of g ( x ) 3) ∫ cos f ( x ) d x = sin f ( x ) f ′ ( x ) + C Calculation: Consider, f ( x ) = x 2 ⇒ f ′ ( x ) = 2 x g ( x ) = cos 3 x ⇒ G ( x ) = ∫ cos 3 x d x = 1 3 sin 3 x By using the integration by parts rule, ∫ x 2 cos 3 x d x = x 2 ⋅ ( sin 3 x 3 ) − ∫ 2 x ⋅ ( sin 3 x 3 ) d x = x 2 ⋅ ( sin 3 x 3 ) − ∫ 2 x sin 3 x 3 </

Calculus & Its Applications (14th Edition)

14th Edition

ISBN: 9780134437774

Author: Larry J. Goldstein, David C. Lay, David I. Schneider, Nakhle H. Asmar

Publisher: PEARSON

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Chapter 9, Problem 11RE

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To calculate: The value of an indefinite integral ∫x2cos3x dx

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Chapter 9, Problem 10RE

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Chapter 9 Solutions

Calculus & Its Applications (14th Edition)

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The value of an indefinite integral ∫ x 2 cos 3 x d x

Solution Summary: The author explains how to calculate the value of an indefinite integral, based on the general power rule of integration.

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To calculate: The value of an indefinite integral ∫x2cos3x dx

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Chapter 9 Solutions