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The various parts of an integral have special meaning. Using
the audio notation would produce a rendering that cues the
subscript and superscript on the integral, leaving it to the
listener to interpret their meaning. Rule *descriptive*
for object *integral* (see fig:descriptive-integral)
interprets the subscript and superscript as the limits of
integration. Integrals having no superscript are interpreted as
surface integrals. The rule also correctly identifies the
variable of integration in the majority of examples.

**:** Descriptive rendering rule for
integrals.

We have a similar rendering rule for summations that interprets the subscript as a constraint on the summation. The rule also correctly renders examples where the subscript and superscript to the summation operator give the lower and upper bound on the range of summation.

TV Raman

Thu Mar 9 20:10:41 EST 1995