Use of brackets around the integrand

Question

Quick notation question:

When using brackets after an integral sign, should the brackets enclose just the integrand or everything - the integrand and the differential, i.e. is it:

$$\int \left[f(x)\right] \; dx$$

Or

$$\int \left[f(x) \; dx\right]$$

---

Background:

A friend of mine is writing a report where he has the equation:

$$I = I_{0}e^{-\int f(x,y) \; ds}$$

In standard LaTeX produced by pdflatex (sc. not in MathJaX where it actually looks a little better in my opinion), the integral sign is very similar to the $f$ and I myself find the result a little unclear. I considered using brackets, but I wasn't sure whether it should be:

$$I = I_{0}e^{-\int \left[f(x,y)\right] \; ds}$$

Or

$$I = I_{0}e^{-\int \left[f(x,y) \; ds\right]}$$

Answer 1

The parentheses are not necessary. If you insist on using them, they should not enclose the differential in this case of a single argument.

For your typographical problem, like Michael Hardy already commented, often the $\exp$ function is used $$ \exp\left(\int f(x) dx\right) $$ instead of the $e^x$ notation.

In physics some authors prefer a more operator style notation: $$ e^{\int\!dx\,f(x)} \quad \exp\left(\int\!\!dx\,f(x)\right) $$ Otherwise you could experiment with font size adjustments: \begin{array}{cl} e^{\int\!dx\,f(x)} \quad & \\ e^{\normalsize \int\!dx\,f(x)} \quad & \mathtt{\mbox{e^{\normalsize \int\!dx\,f(x)}}} \\ e^{\large \int\!dx\,f(x)} \quad & \mathtt{\mbox{e^{\large \int\!dx\,f(x)}}} \\ e^{\Large \int\!dx\,f(x)} \quad & \mathtt{\mbox{e^{\Large \int\!dx\,f(x)}}} \end{array}

Answer 2

In $\int f(x)\,\mathrm dx$ you may view $f(x)\,\mathrm dx$ as if it is a multiplication. Therefore parentheses are required (not including the $\mathrm dx$) only if you integrate a sum, as in $$\int(x^2+7x)\,\mathrm dx $$ In all other cases, I think parentheses do not add clarity. If $\int$ and $f$ look too similar that may be a problem with non-printing resolutions. Proper spacing may be more essential (and supporting the reader). That being said, I have no problem with the original suggestion (without parentheses). Alternatively, using $\exp$ as suggested in the coments could be adequate.