Explanation Given information : ∫ 0 1 x d x 1 − x 2 Formula Used: a m n = a m / n Negative exponent rule: 1 a m = a − m Power rule of integral: ∫ a b x n ⋅ d x = [ x n + 1 n + 1 ] a b Concept Involved: If ∫ a t f ( x ) ⋅ d x exists for every t > a , then ∫ a ∞ f ( x ) ⋅ d x = lim t → ∞ ∫ a t f ( x ) ⋅ d x provided the limit exists and is finite. If ∫ t b f ( x ) ⋅ d x exists for every t < b , then ∫ − ∞ b f ( x ) ⋅ d x = lim t → − ∞ ∫ t b f ( x ) ⋅ d x provided the limit exists and is finite. If a > 0 then ∫ a ∞ 1 x p d x is convergent if p > 1 and divergent if p ≤ 1 Calculation: Description Steps Rewrite the integral in terms of u, using the u-substitution

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 7.7, Problem 38PS

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Chapter 7.7, Problem 37PS

Chapter 7.7, Problem 39PS

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Chapter 7 Solutions

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

Ch. 7.1 - Prob. 1PS Ch. 7.1 - Prob. 2PS Ch. 7.1 - Prob. 3PS Ch. 7.1 - Prob. 4PS Ch. 7.1 - Prob. 5PS Ch. 7.1 - Prob. 6PS Ch. 7.1 - Prob. 7PS Ch. 7.1 - Prob. 8PS Ch. 7.1 - Prob. 9PS Ch. 7.1 - Prob. 10PS

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Tofind : the value of improper integral if it converges or show that it diverges.

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Chapter 7 Solutions