How to Write Double Integral (∫∫) Symbol in LaTeX
To write double integral symbol (∫∫) in LaTeX, use the LaTeX command \iint. It will add ∫∫ symbol in the text.
In this article, we will discuss how to use calculus double integral symbol (∫∫) in the LaTeX document and its significance in the mathematical expressions and physics.
Symbol Overview
Symbol: Double Integral
Unicode: U+222C
Type: Mathematical
Package Requirement: None (built-in symbol)
Argument: None (no additional arguments needed)
LaTeX Command: \iint
Example: ∫∫
Description
The double integral symbol (∫∫) is built-in symbol available in LaTeX,denoted by command \iint. It is used to represent double integral in mathematics. It is widely used in calculus, differential equations, and various fields of physics.
Syntax
The LaTeX command \iint is used to write the double integral symbol.
\iint
Using the Double Integral Symbol in Mathematical Expression
\documentclass{article}
\begin{document}
$\[ \iint R f(x, y) \, dx \, dy \]$
\end{document}
Output 👇️
∬Rf(x,y)dxdy
In this example, we use the double integral symbol to represent the integration of the function f(x,y) over a region R in the Cartesian plane.
Using the Double Integral Symbol in Physics
\documentclass{article}
\begin{document}
\[ \iint_S \mathbf{F} \cdot d\mathbf{S} \]
\end{document}
Output 👇️
∬SF⋅dS
Here, in the above example, the double integral symbol is used to calculate the flux of the vector field F across a surface S in Physics.
Using the amsmath Package to Use Double Integral Symbol
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\[ \iint_R f(x, y) \, dxdy \]
\end{document}
Output 👇️
∬Rf(x,y)dxdy
In the above example, it uses the amsmath package for mathematical typesetting. In LaTeX document, type \usepackage{amsmath} to use double integral symbol in your document.
Using the mathtools Package to Use Double Integral Symbol
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\[ \iint_R f(x, y) \, \mathrm{d}x \, \mathrm{d}y \]
\end{document}
Output 👇️
∬Rf(x,y)dxdy
Here, in this example, it uses mathtools package for better control of spacing. Type usepackage{mathtools} to use double integral symbol in your document. It provides enhanced control over spacing.
Applications
The double integral symbol has extensive applications various mathematical and scientific fields such as:
- Solve partial differential equations involving two variables.
- Calculation of flux, work, and other physical quantities in physics.
Conclusion
The double integral symbol (∫∫) is a fundamental mathematical symbol used widely in calculus,physics and engineering.
Using the above syntax and examples presented in this article, you can write and use double integral symbol in LaTeX documents to represent the integration and solve complex mathematical expressions.