When reading about an certain algorithm (about parameter estimation for Kalman Filtering page 7 eq 57) I found this notation:

$\int dx f(x)$

which is normally written as $\int f(x) dx$. I spent a significant time to figure this out. Now my question: Why would anybody use such a misleading notation? Is this a convention in certain areas?

I still don't know where the integrand ends and up to now I am pretty convinced that this notation is very harmful, since $\int dx$ also has a meaning.

  • $\begingroup$ I've seen it used in physics sometimes. I don't like it either ;) $\endgroup$ – Marcin Łoś May 13 '14 at 14:01
  • $\begingroup$ One reason people use it is when doing multiple integrals. If you type $\int_0^\pi d\theta \int_0^\infty dr \,e^{-r} \sin^2(\theta)$, then it is easy to match the limits with the variable. $\endgroup$ – Stephen Montgomery-Smith May 13 '14 at 14:08
  • $\begingroup$ @StephenMontgomery-Smith I can see what you mean but when I want the reader to understand it better I write $\int_{\theta = 0}^\pi \int_{r=0}^\infty e^{-r} \sin^2(\theta) dr\:d\theta$ when using multiple integrals. $\endgroup$ – flawr May 13 '14 at 14:24
  • $\begingroup$ @flawr I agree - I do that as well. $\endgroup$ – Stephen Montgomery-Smith May 13 '14 at 14:59

It is often comfortable to use the the notation like $\int dx f(x)$, since it works just like the derivative operate $\frac{d}{dx}$. I emphasizes its function as an antiderivative operator since $\int dx$ and $\frac{d}{dx}$ will cancel out each other directly in front of the function, up to constant.

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