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The extended symbols from txfonts include closed multiple-integral symbols.

Enabling txfonts

To use them, make them accessible from math mode:

\definebodyfont [28pt,24pt,18pt,
  17.3pt,14.4pt,12pt,11pt,10pt,9pt,8pt,7pt,6pt,5pt,4pt] [mm] [
  ex=txex sa 1,
  mc=txexa sa 1]
\setupbodyfont [12pt]

The ex=... definition is not required, but it makes the standard integral symbols the same font as the multiple-integral ones. Then, defined the desired math symbols, for instance:

\definemathsymbol [oiint]               [op] [mc] ["08] [mc] ["09]
\definemathsymbol [oiiint]              [op] [mc] ["29] [mc] ["2a]
\definemathsymbol [ointctrclockwise]    [op] [mc] ["0A] [mc] ["0B]
\definemathsymbol [ointclockwise]       [op] [mc] ["0C] [mc] ["0D]
\definemathsymbol [varointctrclockwise] [op] [mc] ["2B] [mc] ["2C]
\definemathsymbol [varointclockwise]    [op] [mc] ["2D] [mc] ["2E]

\definemathsymbol [iint]                [op] [mc] ["21] [mc] ["22]
\definemathsymbol [iiint]               [op] [mc] ["23] [mc] ["24]
\definemathsymbol [iiiint]              [op] [mc] ["25] [mc] ["26]
\definemathsymbol [idotsint]            [op] [mc] ["27] [mc] ["28]

\definemathsymbol [oiintctrclockwise]   [op] [mc] ["40] [mc] ["41]
\definemathsymbol [oiintclockwise]      [op] [mc] ["48] [mc] ["49]
\definemathsymbol [varoiintctrclockwise][op] [mc] ["4A] [mc] ["4B]
\definemathsymbol [varoiintclockwise]   [op] [mc] ["42] [mc] ["43]

\definemathsymbol [oiiintctrclockwise]  [op] [mc] ["44] [mc] ["45]
\definemathsymbol [oiiintclockwise]     [op] [mc] ["4C] [mc] ["4D]
\definemathsymbol [varoiiintctrclockwise][op] [mc] ["4E] [mc] ["4F]
\definemathsymbol [varoiiintclockwise]  [op] [mc] ["46] [mc] ["47]


The following typesets an integral conservation formula:

  \frac{d}{dt} \iiint_{\Omega} f \,dV
   = \iiint_{\Omega} Q \,dV
    - \oiint_{\partial\Omega} \vec J \cdot \vec{da}