How to code Triple Integral Bounds

Question

$$ \iiint \limits_0^{A} 1\,d\rho\,d\theta\,d\phi $$

The first integral is supposed to go from 0 to A, then second is from 0 to pi, and the third should be from 0 to 1. I couldn't find anything about it online.

Answer 1

Since you appear to prefer placing the limits of integration above and below the integral symbols, I would like to recommend that you "snug up" the integral symbols by inserting \!\! (double negative thinspace) between them.

\documentclass{article}
\usepackage[intlimits]{amsmath}
\begin{document}
[
\int_{0}^{A} !! \int_{0}^{\pi} !! \int_{0}^{1} !   d\rho , d\theta , d\phi
\qquad
\int_{0}^{A} !! \int_{0}^{\pi} !! \int_{0}^{1} 1 , d\rho , d\theta , d\phi
]
\end{document}

Answer 2

I'm not a fan of \limits with \int, unless one wants to just set a domain.

Here's a simplified version, as regards to user level syntax, that automatically computes the number of integral signs to use, based on the list of bounds.

I provide \INT for limits on the side and \INT* for limits above and below.

\documentclass{article}
\usepackage{amsmath}
\ExplSyntaxOn
\NewDocumentCommand{\INT}{sm}
 {
  \kourosh_int:een
   { \IfBooleanT{#1}{\limits} } % \limits for -version
   { \IfBooleanTF{#1}{6}{9} }   % less kerning for -version
   { #2 }
 }
\seq_new:N \l_kourosh_int_in_seq
\seq_new:N \l_kourosh_int_out_seq
\cs_new_protected:Nn \kourosh_int:nnn
 {
  \seq_set_from_clist:Nn \l_kourosh_int_in_seq { #3 }
  \seq_set_map:NNn \l_kourosh_int_out_seq \l_kourosh_int_in_seq { \int#1 ##1 }
  \seq_use:Nn \l_kourosh_int_out_seq { \mspace{-#2mu} }
 }
\cs_generate_variant:Nn \kourosh_int:nnn { ee }
\ExplSyntaxOff
\begin{document}
[
\INT{_0^A,_0^\pi,_0^1} 1,d\rho,d\theta,d\phi
]
[
\INT*{_0^A,_0^\pi,_0^1} 1,d\rho,d\theta,d\phi
]
[
\INT{_0^\pi,_0^1} 1,d\theta,d\phi
]
[
\INT{_0^1} 1,d\phi
]
\end{document}

Answer 3

For a triple integral with bounds I would be more inclined to write

\[
  \int_{0}^{A}  
  \int_{0}^{\pi}
  \int_{0}^{1}
     1\,d\rho\,d\theta\,d\phi
\]

limits style is going to push your limits too close together. It makes more sense if you have something like

\[
   \iiint\limits_{(x,y,z)\in U^3} f(x,y,z) dx\, dy\, dz
\]

Answer 4

Comment came in before I could post..

Yea, that's the answer:

See also: To have two limits in double integral?

MWE

\documentclass[12pt]{article}
\usepackage{amsmath}
\newcommand{\Int}{\int\limits}
\begin{document}
$$\Int_{0}^{A} \Int_{0}^{\pi} \Int_{0}^{1} d\rho; d\theta; d\phi$$
\end{document}