Explanation Given Information: The provided integral is ∫ 0 + ∞ cos x d x . Consider the provided integral, ∫ 0 + ∞ cos x d x . If a function f ( x ) is defined in which the limit is infinite ∫ a + ∞ f ( x ) d x , then the rule is if the limit of the function lim M → + ∞ ∫ a M f ( x ) d x exists, then the function converges, otherwise the function diverges. Determine the limit of the function. ∫ 0 + ∞ cos x d x = lim M → + ∞ ∫ 0 M cos x d x Now, evaluate the integral of the function, by using the formula for the integration of ∫ 0 + ∞ cos x d x = [ sin x ] 0 + ∞ . lim M → + ∞ ∫ 0 M cos x d x = lim M → + ∞ [ sin x ] 0 M Then substitute x = M to determine the value of integral at upper limit

7th Edition

ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 9.3, Problem 56E

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Whether the integral function ∫0+∞cosx dx is converges or not, also find the value of the integral ∫0+∞cosx dx if it converges.

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Chapter 9.3, Problem 55E

Chapter 9.3, Problem 57E

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Chapter 9 Solutions

Applied Calculus

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Whether the integral function ∫ 0 + ∞ cos x d x is converges or not, also find the value of the integral ∫ 0 + ∞ cos x d x if it converges.

Solution Summary: The author explains that if the limit of the integral function is infinite, then the function converges or diverges.

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Whether the integral function ∫0+∞cosx dx is converges or not, also find the value of the integral ∫0+∞cosx dx if it converges.

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Chapter 9 Solutions