How to use the "\limits{}" command with ANY math symbols?

Question

I know \limits can be used to directly place lines under math symbols, but now I want to realise the following effect:

My solution is to define the integrals as a new math operator "\int\cdots\int", but it doesn't seem to work at all...

Answer 1

Combine \overbrace with \mathop.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
=\mathop{\overbrace{\idotsint}^{n-1}}\limits_{x_1^2+\dots+x_n^2\le1}
\]

\end{document}

Maybe with some visual fixes:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\[
=\mathop{\,\,\overbrace{\!\!\idotsint\,}^{n-1}\!}\limits_{x_1^2+\dots+x_n^2\le1}
\]

\end{document}