Aller au contenu

Integrals

Integral expression can be added using the \int_{lower}^{upper} command.

Note, that integral expression may seems a little different in inline and display math mode.

LaTeX code Output
Integral \(\int_{a}^{b} x^2 \,dx\) inside text Example of an integral inside text
\[ \int_{a}^{b} x^2 \,dx \] Example of an integral

Multiple integrals

To obtain double/triple/multiple integrals and cyclic integrals you must use amsmath and esint (for cyclic integrals) packages.

LaTeX code Output
\begin{gather*}
    \iint_V \mu(u,v) \,du\,dv
\\
    \iiint_V \mu(u,v,w) \,du\,dv\,dw
\\
    \iiiint_V \mu(t,u,v,w) \,dt\,du\,dv\,dw
\\
    \idotsint_V \mu(u_1,\dots,u_k) \,du_1 \dots du_k
\end{gather*}
Example of multiple integrals
\[
    \oint_V f(s) \,ds
\]
Example of integrals

Sums and products

Like integral, sum expression can be added using the \sum_{lower}^{upper} command.

LaTeX code Output
Sum $\sum_{n=1}^{\infty} 2^{-n} = 1$ inside text Example of sum expression inside text
\[ \sum_{n=1}^{\infty} 2^{-n} = 1 \] Example of sum expression

In similar way you can obtain expression with product of a sequence of factors using the \prod_{lower}^{upper} command.

LaTeX code Output
Product $\prod_{i=a}^{b} f(i)$ inside text Example of limit expression inside text
\[ \prod_{i=a}^{b} f(i) \] Example of limit expression

Limits

Limit expression can be added using the \lim_{lower} command.

LaTeX code Output
Limit $\lim_{x\to\infty} f(x)$ inside text Example of limits inside text
\[ \lim_{x\to\infty} f(x) \] Example of limits

Examples

Here is an example LaTeX document:

\documentclass{article}
\title{Integrals, Sums and Limits}
\author{Overleaf}
\date{}
\usepackage{amsmath}

\begin{document}

\maketitle

\section{Integrals}

Integral \(\int_{a}^{b} x^2 dx\) inside text.

\medskip

The same integral on display:
\[
    \int_{a}^{b} x^2 \,dx
\]
and multiple integrals:
\begin{gather*}
    \iint_V \mu(u,v) \,du\,dv
\\
    \iiint_V \mu(u,v,w) \,du\,dv\,dw
\\
    \iiiint_V \mu(t,u,v,w) \,dt\,du\,dv\,dw
\\
    \idotsint_V \mu(u_1,\dots,u_k) \,du_1 \dots du_k
\\
    \oint_V f(s) \,ds
\end{gather*}

\section{Sums and products}

Sum \(\sum_{n=1}^{\infty} 2^{-n} = 1\) inside text.

The same sum on display:
\[
    \sum_{n=1}^{\infty} 2^{-n} = 1
\]

Product \(\prod_{i=a}^{b} f(i)\) inside text.

The same product on display:
\[
    \prod_{i=a}^{b} f(i)
\]

\section{Limits}

Limit \(\lim_{x\to\infty} f(x)\) inside text.

The same limit on display:
\[
    \lim_{x\to\infty} f(x)
\]

\end{document}

 Open this example in Overleaf


Further reading

For more information see

Overleaf guides

LaTeX Basics

Mathematics

Figures and tables

References and Citations

Languages

Document structure

Formatting

Fonts

Presentations

Commands

Field specific

Class files

Advanced TeX/LaTeX