Range of the constant of integration

Question

So I was asked this during an examination interview: "Does the constant of integration have a range?"

I am most certain that it doesn't. But the interviewer didn't seem pleased with the answer. So is there really a range of values for the constant of integration?

Answer 1

It can be any real number (corresponding with your answer).

But this can also be rephrased as "its range is $\mathbb R$" (maybe corresponding with what the interviewer had in mind).

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edit:

In my view your answer is correct: a constant is actually not "ranging" over some set. It is not a variable, and even if it was then "domain" would be better than "range".

Answer 2

Your answer is correct: the constant of integration can be any number. Of course, in specific contexts it may be true that a certain constant is more appropiate than another one, but in the general case each constant is as good as any other.

Answer 3

If I understand your question correctly, the constant of integration refers to the $C$ in the following.

$$\frac{dy}{dx}= f(x)$$

$$y = \int f(x) \, dx + C$$

The constant $C$ can be any real number as it will vanish upon differentiation.