Explanation Given information: ∫ cos x x d x Formula: ∫ cos ( u ) d u = sin ( u ) Calculation: Evaluate the integral. ∫ cos x x d x = ∫ cos ( x 1 2 ) x 1 2 d x (1) Assume u = x 1 2 Differentiate the above equation with respect to x. d d x u = d d x x 1 2 d u d x = 1 2 x 1 2 − 1 2 d u = x − 1 2 d x d x = 2 x 1 2 d u Substitute x 1 2 for u and 2 x 1 2 d u for dx in the equation (1)

University Calculus: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780321999580

Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 8.1, Problem 32E

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The value of the integral.

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University Calculus: Early Transcendentals (3rd Edition)

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The value of the integral.

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