Double integral or surface integral is formed by the combination of two integrals. Even if double limit is used without limit, in the case of surface integral, lower limit S and A have to be used. Only S has been passed within the lower limit below.

```
\documentclass{article}
\usepackage{amsmath}
\begin{document}
$$ \iint_S \textbf{F}.d\textbf{S}= \iint\limits_S \textbf{F.n}dS $$
$$ \iint_S \textbf{v}.d\textbf{S}= \iint\limits_S (\textbf{v.n})dS $$
$$ \iint_S f(x,y,z)\;d\sum $$
\end{document}
```

**Output : **

## Double integral[surface integral] symbol with limits in LaTeX

For limit, you have to use subscript and superscript with Integral symbol. You can use `\newcommnad`

instead of typing the same expression over and over again.

```
\documentclass{article}
\begin{document}
$$ 2\int_0^{2\pi}\int_0^1 e^3 \cos\theta.r\;\sin\theta\; r\;dr\;d\theta $$
$$ I=\int_0^{2\pi}\int_0^{\sqrt{2}}r^3\sqrt{1+4r^2}\;dr\;d\phi $$
$$ \int_0^1\int_0^{1-y}(4\sqrt{3}\;xy)\;dx\;dy $$
\end{document}
```

**Output : **

To use the limit above and below the integral symbol, you need to use the `\limits`

command separately.

```
\documentclass{article}
\usepackage{amsmath}
\newcommand{\integral}[4]{\int\limits^{#1}_{#2}\int\limits^{#3}_{#4}}
\begin{document}
$$ \integral{\pi}{\theta=-\pi}{2\pi}{\phi=0}\vec{F}.\hat{M}.R^3\;\sin\theta\;d\theta\;d\phi $$
$$ \integral{2\pi}{0}{\frac{\pi}{2}}{0} V(r(\varphi,\theta)) $$
$$ 2\integral{2\pi}{0}{1}{0} e^3 \cos\theta.r\;\sin\theta\; r\;dr\;d\theta $$
\end{document}
```

**Output : **

Of course, you can see by looking at the above two outputs, in which case using the `\limits`

command would be the best practice!

## Surface closed integral symbol in LaTeX

In case of double closed integral, there is no limit. However, S or A is used as a lower limit in the case of surface integral.

```
\documentclass{article}
\usepackage{pxfonts}
\begin{document}
$$ \oiint_{\partial\,\Omega}\textbf{D.}\hat{\textbf{n}}\;dS $$
$$ \oiintclockwise,\oiintctrclockwise $$
\end{document}
```

**Output : **