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?
Thanks.

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

Calculus 
charlie,
Thanks that was quick!
Therefore, given my scenario, I could use the integral to calculate the area under the curve described by the derivative?
Charlie. 
Calculus 
charlie,
"My reasoning is that 'undoing' the derivative gives me the derivative."
oops, meant to write
......gives me the integral. 
Calculus 
drwls,
That is what I assumed you meant; I should have read your reasoning more closely. Anyway, you got it right

Calculus 
charlie,
Great, and thank you very much.
Charlie.