:The average distance between two randomly chosen points in the unit square is given as a quadruple integral.
2.
It may be easier to picture curved space-time or quadruple integrals ( as well as integrals over a 3-dimensional " supersurface " in 4-dimensional space, just like surface integrals over 2-dimensional surfaces in 3-dimensional space ).
3.
I Googled and found mention of using quadruple integrals for " determining the interference between elements of a compound array of radiating elements " ( ), but besides some other obvious cases like four-dimensional Euclidean space, I couldn't really find real-life applications of a quadruple Riemann integral.
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