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6.7: The Antiderivative (Indefinite Integral)

  • Page ID
    2071
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    Notice something important here: taking the derivative of f(x) may precisely give you g(x), but taking the antiderivative of g(x) does not necessarily give you f(x) in its original form. Example:

    11054.png

    Note that the constant c is unknown! The original function f(x) could have been 3x2 + 5, 3x2 + 10, 3x2 + anything, and the derivative of f(x) would have still been 6x. Determining the antiderivative of a function, then, is a bit less certain than determining the derivative of a function.


    6.7: The Antiderivative (Indefinite Integral) is shared under a GNU Free Documentation License 1.3 license and was authored, remixed, and/or curated by Tony R. Kuphaldt via source content that was edited to conform to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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