Antiderivative

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The slope field o F(x) = (x3/3)-(x2/2)-x+c, shawin three o the infinitely mony solutions that can be produced bi varyin the arbitrary constant C.

In calculus, an antiderivative, primitive function, primitive integral or indefinite integral[Note 1] o a function f is a differentiable function F whase derivative is equal tae the oreeginal function f. This can be statit seembolically as F = f.[1][2]

Notes[eedit | eedit soorce]

  1. Antiderivatives are also called general integrals, an sometimes integrals. The latter term is generic, an refers nae anly tae indefinite integrals (antiderivatives), but an aa tae definite integrals. When the wird integral is uised wioot addeetional specification, the reader is supposed tae deduce frae the context whether it is referred tae a definite or indefinite integral. Some authors define the indefinite integral o a function as the set o its infinitely mony possible antiderivatives. Ithers define it as an arbitrarily selectit element o that set. Wikipaedia adopts the latter approach.[citation needit]

References[eedit | eedit soorce]

  1. Stewart, James (2008). Calculus: Early Transcendentals (6th ed.). Brooks/Cole. ISBN 0-495-01166-5. 
  2. Larson, Ron; Edwards, Bruce H. (2009). Calculus (9th ed.). Brooks/Cole. ISBN 0-547-16702-4.