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 \(\int_{a}^{b} x^2 ,円dx\) inside text |
[画像:Example of an integral inside text] |
\[ \int_{a}^{b} x^2 ,円dx \] |
[画像: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) ,円du,円dv \\ \iiint_V \mu(u,v,w) ,円du,円dv,円dw \\ \iiiint_V \mu(t,u,v,w) ,円dt,円du,円dv,円dw \\ \idotsint_V \mu(u_1,\dots,u_k) ,円du_1 \dots du_k \end{gather*} |
[画像:Example of multiple integrals] |
\[ \oint_V f(s),円ds \] |
[画像: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 |
[画像:Example of sum expression inside text] |
\[ \sum_{n=1}^{\infty} 2^{-n} = 1 \] |
[画像: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 |
[画像:Example of limit expression inside text] |
\[ \prod_{i=a}^{b} f(i) \] |
[画像: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 |
[画像:Example of limits inside text] |
\[ \lim_{x\to\infty} f(x) \] |
[画像: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: \[ \int_{a}^{b} x^2,円dx \] and multiple integrals: \begin{gather*} \iint_V \mu(u,v) ,円du,円dv \\ \iiint_V \mu(u,v,w) ,円du,円dv,円dw \\ \iiiint_V \mu(t,u,v,w) ,円dt,円du,円dv,円dw \\ \idotsint_V \mu(u_1,\dots,u_k) ,円du_1 \dots du_k \\ \oint_V f(s) ,円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}
Further reading
For more information see