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Antiderivatives

  • Titu Andreescu
  • Cristinel Mortici
  • Marian Tetiva
Chapter

Abstract

An antiderivative of the function f: I ⊆  →  is a differentiable function F: I → , such that F  = f. If F is an antiderivative of f, then F + c is also an antiderivative of the function f, for every real constant c. In fact, when I is an interval (and in most cases it is), these functions F + c, c ∈ , are all the antiderivatives of f. (This is because if F and G are two antiderivatives for the same function f on the interval I, then the derivative of GF vanishes on I; therefore the difference GF must be a constant. Note the importance of the fact that I is an interval.) We denote by

Keywords

Positive Integer Continuous Function Real Function Differentiable Function Positive Real Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media LLC 2017

Authors and Affiliations

  • Titu Andreescu
    • 1
  • Cristinel Mortici
    • 2
  • Marian Tetiva
    • 3
  1. 1.University of Texas at Dallas Natural Sciences and MathematicsRichardsonUSA
  2. 2.Valahia University of TargovisteTargovisteRomania
  3. 3.Gheorghe Rosca Codreanu National CollegeBarladRomania

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