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Why output of \int defer when used in $$--$$ vs align? How to make output from latter look more like former?

\documentclass{article}
\usepackage[utf8]{inputenc}

\begin{document}
$$\int_V \mu(u,v,w) \,du\,dv\,dw $$
\begin{align}
  \int_V \mu(u,v,w) \,du\,dv\,dw
\end{align}
\end{document}

enter image description here PS: I am typesetting on overleaf.

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  • 5
    Welcome! I get the expected size of \int. Please, make a complete example reproducing the issue, from \documentclass to \end{document}
    – egreg
    Apr 4 '20 at 19:51
  • 5
    Welcome! You should not use $$ ... $$ anyway (and it helps the readers tremendously if differential d's are upright).
    – user194703
    Apr 4 '20 at 19:56
  • 4
    Are you by any chance comparing $\int$ (one pair of dollars) with the display math version that you get with the align environment? Apr 4 '20 at 19:58
  • 2
    the left hand version is the inline math with single dollar. Please always post a complete small document that shows the problem, that avoids this kind of error in the question. Apr 4 '20 at 20:55
  • 1
    @Schrödinger'scat don't let egreg see you ask for upright d, he'll get very cross. Apr 4 '20 at 20:55
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The problem can be reproduced from your code. However, the LaTeX run shows several errors:

! LaTeX Error: Environment align undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...

l.6 \begin{align}

After this error, TeX tries to recover as best it can.

You need \usepackage{amsmath} in the document preamble.

Besides, never use $$ in LaTeX, see Why is \[ ... \] preferable to $$ ... $$?

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation*}
\int_V \mu(u,v,w) \,du\,dv\,dw
\end{equation*}
Some text in between.
\begin{align}
  \int_V \mu(u,v,w) \,du\,dv\,dw
\end{align}

\end{document}

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