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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?

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

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?

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