# How do you write an integral and why

A. Year 1 Calculus Student Approach $$F(x) = \int f(x') dx\,$$

B. Random math paper you find online approach $$F(x) = \int dx f(x') \,$$

C. Spivak $$F(x) = \int f(x) \,$$

D. ???

(Edit) I'm asking because I read a post on Math Stackexchange that said something about dropping the dx is totally fine because it is not well defined. I'm curious as to what real mathematicians do.

• $$\int f(x)\,dx.$$ There's no ambiguity about order of integration or what the variable being integrated is or anything of that sort. Most mathematicians will use this notation. Physicists tend to like the second notation for whatever reason (as a former physicist, I don't even understand the appeal). – Cameron Williams Aug 1 '14 at 1:05
• I think Spivak actually writes $\int f$, not $\int f(x)$, but I may be wrong. – Ian Mateus Aug 1 '14 at 1:07
• You can't drop $dx$ in general. Think of $\int xy.$ Then $\int xy dx$ is completely different from $\int xy dy$ or $\int xy dt.$ If you work with only a variable, say $x,$ and this is assumed you could drop $dx,$ although I am not sure if this is standard. – mfl Aug 1 '14 at 1:11
• It's standard to drop the $d$_ if there's no ambiguity. This is because mathematicians can be lazy with respect to these things. – A. Barron Aug 1 '14 at 1:15
• Does anyone ever use B? If so, are you trying to make explicit that the integral is an operator that operates on f? – Carlos - the Mongoose - Danger Aug 1 '14 at 1:17

I personally prefer the following notation for integration $\int f(x)\ dx$ I try to leave no room for ambiguity and to me this notation makes the integral clear, explicit and easily understood. Also the $dx$ can be read as "with respect to $x$".