Integrals, sums and limits

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


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