A similar problem appeared in the Technology Review Puzzle Corner, circa 1975: Consider a domino, two adjacent 1x1 squares. What's the average distance between a random point in the left square, and a random point in the right square? We did it by hand, and the answer was in closed form, but a mess. I found that Macsyma of that era could do most of the integral, with hand-holding, but ran into a problem at the final level. It turns out that being able to answer the puzzle for two random points in a rectangle is enough to answer it for any two (orthogonally oriented) rectangles in the plane. Math needs to deal better with made-up functions like this. The closed form answers are something of a distraction: too complex, not especially informative. Consider the 3-D version of this puzzle, which might be relevant in modeling random gasses. Rich ________________________________________ From: math-fun-bounces@mailman.xmission.com [math-fun-bounces@mailman.xmission.com] On Behalf Of N. J. A. Sloane [njas@research.att.com] Sent: Thursday, February 28, 2008 9:40 AM To: math-fun@mailman.xmission.com Cc: njas@research.att.com Subject: [math-fun] Re help with definite integral The other day I asked for help in evaluating a definite integral Let h = 1/2, to save space. Int_{x = 0..h} Int_{r=-h-x..h-x} Int_{y=0..h} Int_ {s=-h-y..h-y} sqrt(r^2+s^2) dx dr dy ds = ? Thanks to David Cantrell, Eric Weisstein, Steve Finch, Emeric Deutsch and others who replied. To summarize the results: Integrals like this can be found in the books Finch, Encyclop. of Math. Constants (CUP); Santalo, Integral Geometry (Addison-Wesley) There is a web page in Spanish: <http://groups.google.com/group/es.ciencia.matematicas/browse_frm/thread/efec... d222ada58ab7> Mathematica can do this integral, but you have to put the variables in the right order, and you need a machine with the right operating system (it worked on a Sun Linux 64-bit machine, but - with the same version of Mma - failed on an Intel-based Linux 64-bit machine) Best regards Neil _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun