How to Write the Average Integral Symbol in LaTeX

The average integral symbol is an integral sign with a bar or slash through it. In LaTeX, a straightforward way to produce a dashed version is to load the esint package and use \dashint. This article shows a complete example, explains what the notation usually means, and notes an alternative command.

Use \dashint from esint

Add esint to the preamble, then use \dashint just as you would use \int. Subscripts and limits work in the usual way:

\documentclass{article}
\usepackage{esint}

\begin{document}

\[
  \dashint_a^b f(x)\,\mathrm{d}x
\]

\end{document}

Compile this example with a standard LaTeX engine such as pdfLaTeX. The \, adds a small space before the differential, and \mathrm{d} keeps the differential upright. The esint package also provides other extended integral symbols. It can change the appearance of ordinary integral signs as well, so check that its glyphs fit the rest of your document.

What the average integral means

The symbol often indicates that the integral has been normalized by the size of its domain. For an ordinary interval with $a<b$ and an integrable function $f$, a common convention is to define its value as

For example, the average value of $f(x)=x$ on $[0,2]$ is

More generally, for an integrable function $f$ on a domain $E$ with finite, nonzero measure $\mu(E)$, an average integral may mean

The symbol alone does not fix the definition in every field. Check the surrounding text or the author’s stated convention, especially for domains with infinite measure or specialized uses in analysis.

Alternative: \fint from nccmath

The nccmath package provides a \fint command for an average integral. For example, load \usepackage{nccmath} and write \fint_a^b f(x)\,\mathrm{d}x. Its glyph can differ from the one produced by \dashint.

Choose the command that matches the symbol style used in your document. Avoid loading multiple packages just to obtain the same symbol without checking for conflicts or changes to other math symbols. If a journal or textbook specifies a particular notation, follow its convention.

Common mistakes

• Using \int when you mean an average. An ordinary integral gives accumulated quantity; it is not divided by the domain’s length or measure unless you include that factor.
• Assuming every dashed integral has the same meaning. Authors use barred or slashed integral signs differently. Define the notation if readers might not know which convention you intend.
• Typing the Unicode symbol directly. A character such as ⨍ may not be supported by the selected engine or math font. A LaTeX command is generally more portable.
• Expecting identical glyphs from different packages. \dashint and \fint can have different designs and spacing. Compile a small test document to see which suits your output.