# What is the indefinite integral of zero? [duplicate]

From the definition of indefinite integral I might say: Since the derivative of a constant is zero, thus the indefinite integral of zero is a constant. Therefore: $$\frac{dc}{dx} = 0 \quad\iff\quad \int 0dx = c, \quad\forall c\in\mathbb{R}$$

However... we know that $0\in\mathbb{R}$, and since zero is a constant, I can pull it out the integral: $$\int 0dx = 0\cdot\int 1dx = 0\cdot(x+c) = 0$$

And then we end up that integral of zero is zero, not an arbitrary constant. Where is wrong here?

• This is great fun! Dec 15, 2014 at 20:17
• I think treating zero as a constant isn't right, since it's a determined value. Dec 15, 2014 at 20:26
• @alexjo The title is somehow coincidentally identical to this question, true. But, I'm actually asking a different thing. Dec 15, 2014 at 20:28
• @Physicist137 Did you read the most up-voted answer? It deals with your question.
– Eff
Dec 15, 2014 at 20:30
• @Physicist137 If you haven't read it, Sam DeHority answered your question as well though. Dec 15, 2014 at 20:30