Explanation Given information: Given functions are f ( x ) = 1 − 1 x 2 and g ( x ) = 1 x + x Calculation: Given F ' ( x ) = f ( x ) Hence, F ( x ) = ∫ f ( x ) d x The antiderivative of the given function can be written as: ∫ f ( x ) d x = ∫ 1 − 1 x 2 d x ∫ f ( x ) d x = ∫ 1 d x − ∫ x − 2 d x ∫ f ( x ) d x = 1 ⋅ x − x − 2 + 1 − 2 + 1 ∫ f ( x ) d x = x − x − 1 − 1 ∫ f ( x ) d x = x − ( − 1 x ) ∫ f ( x ) d x = x + 1 x + C Where C is a constant

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 6.2, Problem 46P

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To find the antiderivative of the given function and to check if there is only one possible solution.

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Chapter 6.2, Problem 45P

Chapter 6.2, Problem 47P

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To find the antiderivative of the given function and to check if there is only one possible solution.

Solution Summary: The author explains that g(x) is the antiderivative of the given function.

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Chapter 6 Solutions