Explanation Given data: y If g ′ ( x ) = h ( x ) , then is g an antiderivative of h or h is antiderivative of g ? Method/Formula used: Definition of derivative and antiderivative. Let f ( x ) be a function, the indefinite integral of which is given by F ( x ) = ∫ f ( x ) d x + C , then F ′ ( x ) = d d x ( ∫ f ( x ) d x + C ) = d d x ( ∫ f ( x ) d x ) + d d x C = f ( x ) + 0 ⇒ F ′ ( x ) = f ( x ) or d d x ( F ( x ) ) = f ( x )

14th Edition

ISBN: 9781464151088

Author: Associate Professor Laura Taalman, Peter Kohn

Publisher: W.H. Freeman & Company

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Chapter 4.4, Problem 1TB

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To find:Whether the given function is derivation or antiderivative.

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Chapter 4.3, Problem 4TF

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Whether the given function is derivation or antiderivative.

Solution Summary: The author explains that the function h(x) is the derivative of a function, the indefinite integral of which is given by

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