How do I stack multiple conditions in a column in math mode? [duplicate]

Question

I am experimenting with multiple integrals and volume (and area) elements.

I can write the integral,

$A = \int_a^t{\left|f\left(x\right)\right|dx} $, 

as

$A = \int_a^t{\int_0^{\left|f\left(x\right)\right|} dy \, dx} $ 

but writing it as

$A = \int_{ {a \le s_x \le t} \; \wedge \; {0 \le s_y \le \left|f\left(s_x\right)\right|}} ds$ 

gets ugly and long and I would like to collapse the conditions into a column sort of like with

$A = \int_{ \overset{a \le s_x \le t}{0 \le s_y \le \left|f\left(s_x\right)\right|}} ds$ 

but with both conditions being the same size.

How do I stack multiple conditions in a column in math mode?

Answer 1

The stackengine and mathtools packages might give you more control an the vertical and horizontal spacing. Also, I remove some sputious \left … \right pairs:

\documentclass{article}
\usepackage{mathtools}
\usepackage{stackengine}
\setstackEOL{\\}
\setstackgap{L}{1.8ex}

\begin{document}

\[ A = \int_{\mspace{1mu}\everymath{\scriptstyle }\Vectorstack[l]{a \le s_x \le t\\\mathrlap{0 \le s_y \le |f(s_x)|} }}\, f(s)\,ds \]

\end{document} 

Answer 2

You can use the \substack command to stack multiple conditions; it was originally designed for limits of operators, e.g. \sum_{\substack{j=1 \\ j\ne i}}, but works well for integrals too:

\int\limits_{\substack{a\le s\le t\\ 0 \le s_y \le |f(s_x)|}
  f(s)\, ds