Notice that, by convention, the double integral has two integral signs, and the triple integral has three; this is a notational convention which is convenient when computing a multiple integral as an iterated integral, as shown later in this article.
22.
LaTeX probably includes \ iiiint for a good reason . 4-dimensional spacetime would be an obvious guess but I'm not sure that it is equivalent to "'R "'4 in the usual sense of defining a multiple integral.
23.
Actually, such a thing does exist : differential forms may have an " exterior derivative " that is again a differential form, and in some sense the body of a multiple integral is a differential form, so you could look for an " exterior antiderivative ".
24.
Her thesis was " Multiple Integrals and Their Geometrical Interpretation of Cartesian Geometry, in Trilinears and Triplanars, in Tangentials, in Quaternions, and in Modern Geometry; Their Analytical Interpretations in the Theory of Equations, Using Determinants, Invariants and Covariants as Instruments in the Investigation ".
25.
In calculus, interchange of the "'order of integration "'is a methodology that transforms iterated integrals ( or multiple integrals through the use of Fubini's theorem ) of functions into other, hopefully simpler, integrals by changing the order in which the integrations are performed.
26.
Multiple integrals extend the dimensionality of this concept : assuming an-dimensional analogue of a rectangular Cartesian coordinate system, the above definite integral has the geometric interpretation as the-dimensional hypervolume bounded by and the axes, which may be positive, negative, or zero, depending on the function being integrated ( if the integral is convergent ).
27.
I guess from the last bit of the original solution that \ int _ 0 ^ { \ infty } e ^ {-r ^ 2 } r \ dr \ evaluates to 1 / 2, but I'm not sure how that comes about, as it seems to be of the same form as the original problem, unless there's something about the multiple integrals I'm not getting . 80.169.64.22 20 : 58, 1 July 2007 ( UTC)
