Explanation Given information: s + 1 ( 4 − s 2 ) 1 / 2 Formula: ∫ c d 1 a 2 − x 2 d x = [ sin − 1 x a ] c d ∫ c d 1 x n d x = [ x − n + 1 − n + 1 ] c d Calculation: Express the integral as below. ∫ 0 2 s + 1 ( 4 − s 2 ) 1 / 2 d s = ∫ 0 2 [ s ( 4 − s 2 ) 1 / 2 + 1 ( 4 − s 2 ) 1 / 2 ] d s (1) Assume the variable u as u = 4 − s 2 Differentiate the above equation. d u d s = − 2 s − d u 2 = s d s When the value of s is 0, the value of u is 4 . When the value of s is 2, the value of u is 0. Substitute − d u 2 for s d s and u for 4 − s 2 and change the limits in the first term of RHS in equation (1)

University Calculus: Early Transcendentals (4th Edition)

4th Edition

ISBN: 9780134995540

Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.

Publisher: PEARSON

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Chapter 8.7, Problem 16E

To determine

The improper integral without using tables.

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Chapter 8.7, Problem 15E

Chapter 8.7, Problem 17E

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University Calculus: Early Transcendentals (4th Edition)

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