To write multiple integral in latex, intuitive way is to use \int several times like
\begin{equation}
\int\int_{S} f(x,y)dxdy
\end{equation}
This code provides awful spacing between neighboring integral symbols. Alternative way is to use \iint of amsmath package like
\usepackage{amsmath}
\begin{equation} \iint_{S} f(x,y)dxdy \end{equation}
