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If I have a function f(x), and am given its derivative, f'(x): may I take it as a given that f(x) is an integral of f'(x).

My reasoning is that 'undoing' the derivative gives me the derivative.

Eg is 1/3x^3 an integral of x^2?


  • Calculus -

    Yes to both your answers and your reasoning. An arbitrary constant can always be added to the integral, however.

  • Calculus -

    Thanks- that was quick!

    Therefore, given my scenario, I could use the integral to calculate the area under the curve described by the derivative?


  • Calculus -

    "My reasoning is that 'undoing' the derivative gives me the derivative."

    oops, meant to write me the integral.

  • Calculus -

    That is what I assumed you meant; I should have read your reasoning more closely. Anyway, you got it right

  • Calculus -

    Great, and thank you very much.


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