[Tex/LaTex] surface integral

symbols

I can do a path integral like this:

$$\oint \limits_{C(S)} fd{\textbf l}$$

But how can I do a surface integral? The output should look something the surface integrals below, but hopefully better:

enter image description here

Best Answer

A version where the limits are underneath the integral signs:

\documentclass{article}

\usepackage{amsmath,esint}

\newcommand*\VF[1]{\mathbf{#1}}
\newcommand*\dif{\mathop{}\!\mathrm{d}}

\begin{document}

\begin{align*}
  \iiint\limits_V (\nabla \cdot \VF{F}) \dif V
  &= \oiint\limits_{S(V)} \VF{F} \cdot \hat{\VF{n}} \dif S\\
  \iiint\limits_V (\nabla \times \VF{F}) \dif V
  &= \oiint \hat{\VF{n}} \times \VF{F} \dif S
\end{align*}

\end{document}

output1

A version where the limits are beside the integral signs:

\documentclass{article}

\usepackage{amsmath,esint}

\newcommand*\VF[1]{\mathbf{#1}}
\newcommand*\dif{\mathop{}\!\mathrm{d}}

\begin{document}

\begin{align*}
  \iiint_{V} (\nabla \cdot \VF{F}) \dif V
  &= \oiint_{S(V)} \VF{F} \cdot \hat{\VF{n}} \dif S\\
  \iiint_{V} (\nabla \times \VF{F}) \dif V
  &= \oiint \hat{\VF{n}} \times \VF{F} \dif S
\end{align*}

\end{document}

output2

Note: As pointed out by Charles Staats, the upright d in a differential is not common notation in all branches of science; for an italic d, simply use a d without \mathrm.

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