# Volume integrals in Content MathML

From: JB Collins <joebmath@yahoo.com>
Date: Mon, 3 Nov 2008 18:19:34 -0800 (PST)

Message-ID: <578955.35486.qm@web57606.mail.re1.yahoo.com>
Assume that the mass of an object is given by the volume integral of its mass density.
In LaTeX:

$\int \rho({\bf r}) d^3{\bf r}$

The (unambiguous) interpretation of this is the integration of the density over all 3-space, regardless of the basis in which the vector, r, may later be expressed.

Can this be expressed in Content MathML compactly, without the assumption of a basis?

Certainly if I assume a basis, e.g., Cartesian coordinates, then I could express the integral as

<apply>
<int/>
<bvar> <ci>x</ci> </bvar>
<lowlimit><minfinity/></lowlimit>
<uplimit><infinity/></uplimit>
<apply>
<int/>
<bvar> <ci>y</ci> </bvar>
<lowlimit><minfinity/></lowlimit>
<uplimit><infinity/></uplimit>
<apply>
<int/>
<bvar> <ci>z</ci> </bvar>
<lowlimit><minfinity/></lowlimit>
<uplimit><infinity/></uplimit>
<apply>
<fn>&rho</fn>
<vector> <ci>x</ci> <ci>y</ci> <ci>z</ci> </vector>
</apply>
</apply>
</apply>
</apply>

Regards,
Joe C.


Received on Tuesday, 4 November 2008 02:20:23 UTC

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