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.

**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

1999-05-26