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).

Question

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

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

Thanks.

Answer 1

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

Answer 2

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

oops, meant to write

......gives me the integral.

Answer 3

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.

Answer 4

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

Answer 5

Great, and thank you very much.

Charlie.