How to Format Integral Symbols in LaTeX

LaTeX formats an ordinary integral with the \int command. You can add lower and upper bounds using a subscript and a superscript, and choose whether those bounds sit beside the integral sign or above and below it.

The examples below use the amsmath package for multiple-integral commands; stacked limits use the standard \limits modifier. The basic \int command does not require a special package.

Basic integral syntax

Write the lower bound with _ and the upper bound with ^:

\int_{a}^{b} f(x)\,dx

This produces an integral from $a$ to $b$. The \, inserts a small space before the differential, which separates it visually from the integrand. You can omit braces around a single character or a single command, as in \int_0^1; braces are clearer and needed to group a bound made of multiple tokens or a compound expression.

Use \int for an ordinary integral, \oint for a closed contour integral, and—when you load amsmath—commands such as \iint and \iiint for double and triple integrals. For example:

\iint_D f(x,y)\,dA

Put bounds beside or above the symbol

For integral signs, LaTeX normally puts bounds to the right of the symbol, including in displayed equations. This differs from operators such as \sum, whose bounds are usually placed above and below in display math.

To force the bounds above and below an integral, use \limits immediately after the command:

\int\limits_{a}^{b} f(x)\,dx

To explicitly keep them beside the symbol, use \nolimits:

\int\nolimits_{a}^{b} f(x)\,dx

The usual side placement is compact and works well for most integrals. Above-and-below placement can be useful when the bounds need emphasis or when a particular display style calls for it. In inline math, forcing limits above and below can make the line taller, so use it selectively.

Complete compilable example

This example shows an inline integral, a displayed calculation, both limit placements, and several integral types.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

Inline: $\int_0^1 x^2\,dx$.

\[
  \int_0^1 x^2\,dx
  = \left[\frac{x^3}{3}\right]_0^1
  = \frac{1}{3}.
\]

\[
  \int\limits_0^1 x^2\,dx
  \qquad
  \int\nolimits_0^1 x^2\,dx
\]

\[
  \iint_D f(x,y)\,dA,
  \qquad
  \iiint_V g(x,y,z)\,dV,
  \qquad
  \oint_C \mathbf{F}\cdot d\mathbf{r}.
\]

\end{document}

The amsmath package provides \iint and \iiint, among other mathematical tools. The \left[ and \right] commands size the evaluation brackets to fit the expression between them. The \qquad commands add horizontal space between examples; they are only for visual separation, not part of integral syntax.

For a larger integral sign inside an inline expression, you can use \displaystyle, for example $\displaystyle \int_0^1 x^2\,dx$. This changes the math style and enlarges the symbol, but it does not by itself move integral bounds above and below. Use \limits when you want that placement.

Common formatting mistakes

• Forgetting braces around a multi-part bound: \int_0^n+1 treats only the 0 as the subscript. Write \int_{0}^{n+1} to make the full bound clear.
• Using \limits on the wrong command: Put it directly after the integral operator and before its scripts: \int\limits_{a}^{b}.
• Leaving no separation before the differential: f(x)dx can look crowded. The conventional form is f(x)\,dx. If your style guide calls for an upright differential, write f(x)\,\mathrm{d}x instead.
• Typing repeated ordinary integrals for a multiple integral: Prefer \iint or \iiint rather than \int\int or \int\int\int. The dedicated commands give the conventional multiple-integral symbols and spacing.
• Expecting \displaystyle to stack the bounds: It enlarges the integral in inline math, but \limits controls whether the bounds go above and below.

When you need a different integral symbol

The commands above cover common integral notation. Specialized symbols—such as an average integral or some surface and volume integrals—may require a dedicated package or a custom definition. Choose a symbol that matches the mathematical notation you intend, and check the package documentation for the command and required setup. Avoid building a new glyph by overlaying unrelated symbols unless you have to; spacing and alignment can vary across fonts and math styles.