Contour Integral Symbol ∮

The contour integral is a concept in complex analysis that involves integrating a complex-valued function along a curve or path in the complex plane. It plays a crucial role in the study of complex analysis and has applications in physics and engineering.

Definition

The contour integral is denoted by the symbol ∮ and is expressed as ∮ f(z) dz, where f(z) is a complex-valued function of a complex variable z, and dz represents the differential along the contour.

Representation in HTML

In HTML, the contour integral symbol can be represented using the HTML entity ∮.

Usage in Mathematics

Contour integrals are used to evaluate complex integrals and are especially powerful when applied to functions with singularities or complex paths in the complex plane. They are widely used in physics, particularly in the study of fluid dynamics and quantum mechanics.

Example

An example of a contour integral might involve integrating a function f(z) along a closed path in the complex plane, such as a circle or a square.

Understanding the contour integral is essential for mathematicians and scientists working in fields where complex analysis is applied. It provides a powerful tool for solving problems involving complex functions and integrals.

Contour Integral Symbol Information

Symbol Name	Contour Integral
Unicode Version	1.1 (June 1993)
Unicode	U+222E
CSS Code	\222E
HTML Entity	&ContourIntegral;

Hex Code	∮
HTML Code	∮
Latex	\oint
Symbol	∮

Contour Integral Symbol Encoding

UTF-8	0xE2 0x88 0xAE
UTF-16	0x222E
UTF-32	0x0000222E

Contour IntegralSymbol's PNG and SVG files

Contour Integral Symbol in Latex

Contour Integral

\documentclass{article}
\begin{document}
\oint
\end{document}

How to add contour integral symbol via keyboard on different Operating systems

You can type the contour integral symbol on most modern devices with the help of following methods:

How to type contour integral symbol on Microsoft Word

You can type the contour integral in Microsoft Word using steps mentioned below:

Place your cursor in the text area where you need to insert the symbol and type 222E
Without moving the cursor press keys Alt + x together
The original 222E is now transformed into ∮

How to type contour integral symbol on Microsoft Windows

You can type the contour integral on Microsoft windows using following steps:

Hold Alt and press to type contour integral on your windows machine.

How to type contour integral symbol on Mac OS

You can type the contour integral on Mac OS using following steps:

Place your cursor in the text area where you need to insert the symbol
Press Ctrl + ⌘ Command + ⎵ Space to bring up the Character Viewer. Alternatively, choose Edit ⇒ Emoji & Symbols
Type "Contour Integral" in the search field at the top and press Enter
The symbol should appear. Click on it to insert it into your text

How to type contour integral symbol on Linux

You can type the contour integral on Linux using following steps:

Place your cursor in the text area where you need to insert the symbol
Hold ⇧ Shift + Ctrl and press the letter + U
Press keys 222E consecutively
And then press ↵ Enter , the desired symbol will be added to your document

How to type contour integral symbol on IOS and Android

The easiest way to type the contour integral symbol on ios and android is to copy and paste it wherever you need it.

How to use contour integral in CSS

//CSS Example

span {
    content: \222E;
  }

How to use contour integral in HTML

//HTML Example

<span>&#8750;</span>

Contour Integral symbol representation in programming languages

Contour Integralsymbol's representation in different programming languages can be found in table below:

Language	Representation
Rust	\u{222E}
Ruby	\u{222E}
Python	\u222E
PHP	\u{222E}
Perl	\x{222E}
Java	\u222E
Modern JavaScript - Since ES6	\u{222E}
JavaScript	\u222E
Go	\u222E
C#	\u222E
C and C++	\u222E
Bash and Zsh - inside echo -e	\u222E
RFC 5137	\u'222E'