Posted by **charlie** on Saturday, September 15, 2007 at 7:52am.

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?

Thanks.

- Calculus -
**drwls**, Saturday, September 15, 2007 at 7:54am
Yes to both your answers and your reasoning. An arbitrary constant can always be added to the integral, however.

- Calculus -
**charlie**, Saturday, September 15, 2007 at 7:55am
"My reasoning is that 'undoing' the derivative gives me the derivative."

oops, meant to write

......gives me the integral.

- Calculus -
**drwls**, Saturday, September 15, 2007 at 8:01am
That is what I assumed you meant; I should have read your reasoning more closely. Anyway, you got it right

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