Use the wasysym
package (as you do in your document).
\documentclass{beamer}
\usepackage{wasysym}
\begin{document}
\begin{frame}
\[ \iint \vec{v} \circ \mathsf{d}\vec{A} \]
\end{frame}
\end{document}

It is very uncharacteristic to typeset an integral sign uncentered at horizontal math axis. All variable-with math elements like braces, big operators etc are centered in traditional typography.
But if you wish such behaviour then, of course, it is possible. TeX is flexible. You can try the following macros, where \flexibleint
macro is created. Usage is:
\flexibleint_a^b {integrand} or \flexibleint {integrand}
The integrand must be in braces.
\def\tmp#1 #2\relax{#1}
\setbox0=\hbox{$\xdef\intfont{%
\expandafter\tmp\fontname\textfont3\expandafter\space\space\relax}$}
\font\tmp=\intfont\space at10pt\relax
\setbox0=\hbox{$\textfont3=\tmp \displaystyle \int$}
\dimen0=\ht0 \advance\dimen0 by\dp0 \divide\dimen0 by10
\xdef\intsize{\the\dimen0}
\def\dividedimen (#1/#2){\expandafter\ignorept\the
\dimexpr\numexpr\number\dimexpr#1\relax
*65536/\number\dimexpr#2\relax\relax sp\relax
}
{\lccode`\?=`\p \lccode`\!=`\t \lowercase{\gdef\ignorept#1?!{#1}}}
\def\flexibleint{\def\fxintL{}\def\fxintU{}\futurelet\next\fxintA}
\def\fxintA{\ifx\next_\expandafter\fxintB\else\expandafter\fxintC\fi}
\def\fxintB_#1{\def\fxintL{#1}\fxintC}
\def\fxintC{\futurelet\next\fxintD}
\def\fxintD{\ifx\next^\expandafter\fxintE\else\expandafter\fxintF\fi}
\def\fxintE^#1{\def\fxintU{#1}\fxintF}
\def\fxintF#1{\begingroup
\setbox0=\hbox{$\displaystyle{#1}$}%
\dimen0=\ht0 \advance\dimen0 by\dp0
\setbox1=\hbox{$\vcenter{\copy0}$}%
\font\tmp=\intfont\space at\dividedimen(\dimen0/\intsize)pt
\lower\dimexpr\dp0-\dp1\hbox{%
$\textfont3=\tmp \displaystyle\int_{\fxintL}^{\fxintU}$}
\box0
\endgroup
}
$$
X = \sum_{i=0}^\infty
\flexibleint_a^b {u\over {\displaystyle v + {\strut x\over y}}}
$$
\bye

How it works: First, the fontname of \textfont3
(where \int
sign is expected) is extracted at 10pt size (into \intfont
) and the \int
in \displaystyle
at 10pt is measured (in \intsize
).
Secondly, the scanning of _a
or ^b
is performed using auxiliary macros \fxintA
to \fxintE
.
Finally, the integrand in box is measured, its vertically different positions is compared using \box0
and \box1
(the second box is \vcenter
ed), the font for \textfont3
scaled to desired size is temporary loaded and the flexible integral is typeset.
Best Answer
With the help of the
bigints
package (cf. Big integral sign), and some negative space, using Steven's code as a starting point.