Explanation Given information: f ( x ) = x sin π x Formula Used: Integration by parts: If h ( x ) = f ( x ) g ( x ) then ∫ h ( x ) = f ( x ) G ( x ) − ∫ f ' ( x ) G ( x ) d x Where G ( x ) is the antiderivative of g ( x ) and f ' ( x ) is a derivative of f ( x ) . Calculation: Here, f ( x ) = x and g ( x ) = sin π x Consider f ( x ) = x Differentiate with respect to x f ' ( x ) = 1 Now consider g ( x ) = sin π x G ( x ) = ∫ g ( x ) d x = ∫ sin π x d x = − cos π x π By using the formula ∫ h ( x ) = f ( x ) G ( x ) − ∫ f ' ( x ) G ( x ) d x ∫ x sin π x d x = x ( − cos π x π ) − ∫ 1 ⋅ (

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ISBN: 9780137590438

Author: Goldstein

Publisher: PEARSON

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Chapter 9.3, Problem 19E

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To calculate: ∫01x sinπx dx.

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Chapter 9.3, Problem 18E

Chapter 9.3, Problem 20E

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∫ 0 1 x sin π x d x .

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