What is $dx$ in integration? When I was at school and learning integration in maths class at A Level my teacher wrote things like this on the board.
$$\int f(x)\, dx$$
When he came to explain the meaning of the $dx$, he told us "think of it as a full stop".  For whatever reason I did not raise my hand and question him about it.  But I have always shaken my head at such a poor explanation for putting a $dx$ at the end of integration equations such as these.  To this day I do not know the purpose of the $dx$.  Can someone explain this to me without resorting to grammatical metaphors?

I once went at some length illustrating the point that for the purpose of evaluating integrals it is useful to look at $d$ as a linear operator.
