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In a Nut Shell:
The
triple integral of a function, f(x,y,z), gives
the value of the function
integrated over the
region of the volume. The element of volume, dV,
in rectangular
cartesian coordinates can be
expressed as dV
= dx dy dz or in any of six possible
combinations ˗ dx dy dz, dy dx dz, dy dx dz, dy dz dx, dz dx dy, and
dz dy dx .
Cylindrical and
spherical coordinates may also be used during integration and may be
more useful depending
upon the application.
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