Explanation Given information: ∫ 0 1 2 x x 2 + 1 d x Formula used: Change of the 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 ) ) = 1 x 2 + 1 and a = 0 , b = 1 Therefore, g ( x ) = x 2 + 1 At a = 0 ⇒ g ( a ) = g ( 0 ) = ( 0 ) 2 + 1 = 1 and At b = 1 ⇒ g ( b ) = g ( 1 ) = ( 1 ) 2 + 1 = 2 Consider g ( x ) = u = x 2 + 1 Differentiate with respect to x d u d x = 2 x ⇒ d u = 2 x d x As g ( x ) = u = x 2 + 1 ⇒ f ( u ) =

12th Edition

ISBN: 9780137590810

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

Publisher: PEARSON

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Chapter 9.3, Problem 4E

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To calculate: ∫012xx2 + 1dx.

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Chapter 9.3, Problem 3E

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Chapter 9 Solutions

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∫ 0 1 2 x x 2 + 1 d x .

Solution Summary: The author explains the formula used to calculate the displaystyle int: f(x)=1sqr

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Chapter 9 Solutions