posted by charlie on .
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?
Yes to both your answers and your reasoning. An arbitrary constant can always be added to the integral, however.
Thanks- that was quick!
Therefore, given my scenario, I could use the integral to calculate the area under the curve described by the derivative?
"My reasoning is that 'undoing' the derivative gives me the derivative."
oops, meant to write
......gives me the integral.
That is what I assumed you meant; I should have read your reasoning more closely. Anyway, you got it right
Great, and thank you very much.