A repeated integral over variables
is called a multiple integral. An th order integral corresponds, in general, to an -D Volume (Content),
with corresponding to an Area. In an indefinite multiple integral, the order in which the integrals are carried
out can be varied at will; for definite multiple integrals, care must be taken to correctly transform the limits if the order
is changed.
See also Integral, Monte Carlo Integration
References
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. ``Multidimensional Integrals.'' §4.6 in
Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England:
Cambridge University Press, pp. 155-158, 1992.
© 1996-9 Eric W. Weisstein
1999-05-26