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Examples ofantiderivative
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For these potentials, theirantiderivativemay have branches.
From theCambridge English Corpus
The logarithm function, which is the actualantiderivativeof 1/ "x", must be introduced and examined separately.
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This example is from Wikipedia and may be reused under a CC BY-SA license.For a complete list ofantiderivativefunctions, see lists of integrals.
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This example is from Wikipedia and may be reused under a CC BY-SA license.A formula for the integrand may be known, but it may be difficult or impossible to find anantiderivativethat is an elementary function.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The importance of the partial fraction decomposition lies in the fact that it provides an algorithm for computing theantiderivativeof a rational function.
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This example is from Wikipedia and may be reused under a CC BY-SA license.This is because there can be no unique representation of anantiderivativefor inexact differentials since their variation is inconsistent along different paths.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The integral is not actually theantiderivative, but the fundamental theorem provides a way to use antiderivatives to evaluate definite integrals.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The "indefinite integral" is the "antiderivative", the inverse operation to the derivative.
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This example is from Wikipedia and may be reused under a CC BY-SA license.For some elementary functions, it is impossible to find anantiderivativein terms of other elementary functions.
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This example is from Wikipedia and may be reused under a CC BY-SA license.It may be possible to find anantiderivativesymbolically, but it may be easier to compute a numerical approximation than to compute the antiderivative.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Therefore, any constant is anantiderivativeof the zero function.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Furthermore, holomorphy is a necessary condition for a function to have anantiderivative, since the derivative of any holomorphic function is holomorphic.
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This example is from Wikipedia and may be reused under a CC BY-SA license.It is frequently used to transform theantiderivativeof a product of functions into anantiderivativefor which a solution can be more easily found.
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This example is from Wikipedia and may be reused under a CC BY-SA license.It is exact because 1 hasantiderivativex everywhere on the real line.
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This example is from Wikipedia and may be reused under a CC BY-SA license.But if the coefficient 71 is changed to 72, it is not possible to represent theantiderivativein terms of elementary functions.
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This example is from Wikipedia and may be reused under a CC BY-SA license.The most difficult step is usually to find theantiderivativeof "f".
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This example is from Wikipedia and may be reused under a CC BY-SA license.It is rarely possible to glance at a function and write down itsantiderivative.
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This example is from Wikipedia and may be reused under a CC BY-SA license.Using the fundamental theorem of calculus often requires finding anantiderivative.
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This example is from Wikipedia and may be reused under a CC BY-SA license.For example, a "constant of integration" is an arbitrary constant function that is added to a particularantiderivativeto obtain the other antiderivatives.
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This example is from Wikipedia and may be reused under a CC BY-SA license.These examples are from corpora and from sources on the web. Any opinions in the examples do not represent the opinion of the Cambridge Dictionary editors or of Cambridge University Press or its licensors.
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