# The Difference Between Two Indefinite Integrals

1. Dec 30, 2014

I actually came across this question on social media. What is:

$$\int sin (x) \, dx - \int sin (x) \, dx$$

And I think the answer depends on how we interpret:

$$\int sin (x) \, dx$$

If we think of it as a single antiderivative, the answer would be zero. If we think of it as being representative of several antiderivatives of $sin (x)$, the answer would be some arbitrary constant.

What do you think?

Last edited: Dec 30, 2014
2. Dec 30, 2014

### Staff: Mentor

I think "define non-standard or unclear notation if you use it".

3. Dec 30, 2014

### jbstemp

It's standard to evaluate indefinite integrals as the anti derivative of the function plus a constant of integration.

So I think ∫sin(x) dx-∫sinx(x) dx would just be equal to an arbitrary constant (as you said).