Contour Integral in LaTeX (\oint)

Where it is used

Integral sign with a small circle, marking integration around a closed curve.

Complex analysis relies on it heavily: Cauchy's integral theorem says \oint_\gamma f(z)\,dz = 0 for holomorphic f, and the residue theorem evaluates such integrals as 2\pi i times a sum of residues. In physics it appears in circulation and in Ampere's and Faraday's laws, for example \oint_C \mathbf{B}\cdot d\boldsymbol{\ell}. Name the contour in the subscript; \oint_{\partial S} signals the boundary of a surface. A closed surface integral with a circle over two signs is not part of the standard command set, so many authors simply write \iint_{\partial V} and say the surface is closed.

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Contour Integral: $\oint$

\[ \oint_{\gamma} \frac{dz}{z} = 2\pi i \]
\end{document}

Related symbols

• Derivative\frac{d}{dx}
• Triple Integral\iiint
• Partial derivative operator\frac{\partial}{\partial x}
• Double Integral\iint
• Limit\lim_{x \to a}
• Integral\int_{a}^{b}

Frequently asked questions

How do I write Contour Integral in LaTeX?

Type \oint in math mode, for example $\oint_{\gamma} \frac{dz}{z} = 2\pi i$. It works in plain LaTeX without loading any package.

Which package do I need for \oint?

None. \oint is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \oint in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\oint$ in running text. If you only need the glyph in text, paste the Unicode character ∮ instead (with XeLaTeX or LuaLaTeX and a font that has it).