antiderivative

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antiderivative

[¦an·tē·di¦riv·əd·iv]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Calvez, "Orthogonal decomposition of derivatives and antiderivatives for easy evaluation of extended Gram matrix," Signal Processing, vol.
Few of us know precisely what algorithms our CAS uses in determining antiderivatives, or why the CAS may fail to provide an antiderivative on a particular example; however, good facility in hand-computation together with a CAS enables users to handle more sophisticated examples whenever they arise.
On the TI-89 graphics calculator, antiderivatives are determined by substitutions, integration by parts, and partial-fraction expansion, much as described in [3].
It is reasonable to expect that a CAS "simplify" algorithm will often be unable to express an antiderivative using only real elementary functions when such exist, resulting from the complexity of the parameters involved in general hypergeometric functions.
In practice, any CAS will provide a solution to a problem in definite integration when that is all that is required, especially when a closed-form antiderivative is cumbersome.
A function F : T [right arrow] X is called an antiderivative of f: T [right arrow] X provided
(ii) Every ld-continuous function f has a [nabla] antiderivative. In particular if [t.sub.0] [member of] T then F defined by
By using the slider and the trace tool, students can see that the path formed by the values of [[integral].sup.x.sub.a]f(t)dt consists precisely of values of the definite integral, and that this path turns out to be an antiderivative of the original function!