Explanation Given information: ∫ 0 π 2 sin ( 2 x − π 2 ) d x Formula Used: Change of limits rule: ∫ a b f ( g ( x ) ) g ' ( x ) d x = ∫ g ( a ) g ( b ) f ( u ) d u , If g ( x ) = u and g ' ( x ) d x = d u Calculation: Here f ( g ( x ) ) = sin ( 2 x − π 2 ) and a = 0 , b = π 2 Therefore, g ( x ) = 2 x − π 2 At a = 0 ⇒ g ( a ) = g ( 0 ) = 2 ( 0 ) − π 2 = − π 2 and At b = π 2 ⇒ g ( b ) = g ( π 2 ) = 2 ( π 2 ) − π 2 = π 2 Consider g ( x ) = u = 2 x − π 2 Differentiate with respect to x d u d x = 2 ⇒ d u 2 = d x As g ( x ) =

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 9.3, Problem 20E

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To calculate: ∫0π2 sin(2x − π2) dx.

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Chapter 9.3, Problem 19E

Chapter 9.3, Problem 21E

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Chapter 9 Solutions

Calculus & Its Applications (14th Edition)

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∫ 0 π 2 sin ( 2 x − π 2 ) d x .

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Chapter 9 Solutions