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Topic: Antiderivative


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  PlanetMath: antiderivative of complex function
"antiderivative of complex function" is owned by Wkbj79.
Cross-references: open, simply connected, antiderivative, function, analytic function, independent, point, fixed point, path, integral, continuous, satisfies, domain, complex function
This is version 6 of antiderivative of complex function, born on 2005-06-03, modified 2007-05-30.
planetmath.org /encyclopedia/AntiderivativeOfComplexFunction.html   (89 words)

  
  Learn more about Fundamental theorem of calculus in the online encyclopedia.   (Site not responding. Last check: 2007-10-28)
An important consequence of this, sometimes called the second fundamental theorem of calculus, allows one to compute integrals by using an antiderivative of the function to be integrated.
Intuitively, the theorem simply says that if you know all the little instantaneous changes in some quantity, then you may compute the overall change in the quantity by adding up all the little changes.
The version of Taylor's theorem which expresses the error term as an integral can be seen as a generalization of the Fundamental Theorem.
www.onlineencyclopedia.org /f/fu/fundamental_theorem_of_calculus_1.html   (581 words)

  
 PlanetMath: antiderivative
Note that there are an infinite number of antiderivatives for any function
This is version 8 of antiderivative, born on 2002-02-01, modified 2005-03-06.
Object id is 1631, canonical name is Antiderivative.
planetmath.org /encyclopedia/Antiderivative.html   (82 words)

  
 16.1 The Antiderivative
The antiderivative is the name we sometimes, (rarely) give to the operation that goes backward from the derivative of a function to the function itself.
Thus the sentence "the antiderivative of cos x is (sin x) + c" is usually stated as: the indefinite integral of cos x is (sin x) + c, and this is generally written as
The antiderivative of a sum of several terms is the sum of their antiderivatives.
www-math.mit.edu /~djk/calculus_beginners/chapter16/section01.html   (496 words)

  
 Fundamental theorem of calculus - Open Encyclopedia   (Site not responding. Last check: 2007-10-28)
This theorem is of such central importance in calculus that it deserves to be called the fundamental theorem for the entire field of study.
As the derivative of the antiderivative is the original function, F'(c_i) = f(c_i).
If the function g(x) is continuous on some interval [a, b], then there exist infinitely many antiderivatives G(x) whose derivatives are g(x).
open-encyclopedia.com /Fundamental_theorem_of_calculus   (932 words)

  
 Question Corner -- Does Every Function Have an Antiderivative?
I'm interpreting your question to mean "does every function have an antiderivative?", which isn't quite what you wrote, but I think it's what you meant.
However, it may not be possible to express the answer in terms of familiar functions and operations.
to another antiderivative that also cannot be expressed any more simply, but which comes up frequently enough that people have given a special name to it.
www.math.toronto.edu /mathnet/questionCorner/existantideriv.html   (547 words)

  
 Calculus - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-10-28)
More precisely, antiderivatives can be calculated with definite integrals, and vice versa.
It was this realization, made by both Newton and Leibniz, which was key to the explosion of analytic results after their work became known.
The fundamental theorem provides a method to compute many definite integrals algebraically, without performing limit processes, by finding formulae for antiderivatives.
encyclopedia.worldsearch.com /calculus.htm   (1750 words)

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