What's the variable of integration?

[SammyS]

Main Question or Discussion Point

What's the variable of integration???

I keep seeing posts like this:

Help me do this integral

$$\int xe^{-ax}$$

Shouldn't we all ask, right off the bat, "What's the variable of integration?"

Probably what was meant was:

$$\int xe^{-ax}\, dx \,.$$

But maybe the problem actually was:

$$\int xe^{-ax}\, da \,.$$

Does this bother any of you?

 

[CompuChip]

Although it is rather clear what was meant (by the convention of using x for a variable and a for a constant) I agree that the notation is not completely unambiguous.
Depending on the context, it would be important or nit-picky (is that a word?) to point this out to the one who gave you that expression.

 

[Ivan Seeking]

I am reminded of an old physics professor who, when using a dummy variable x for integration of the real variable x, would sheepishly look around the room checking for any math police.

 

[CompuChip]

And if you are really brave, and this were a homework problem, you might just write down
$$\int x e^{ax} = e^{ax} + c$$
(don't forget the + c ) and hand it in like that :)