HP-41 Challenge: Double Integrals by INTEG Recursion

[gjmcclure]

Yes, there are triple, quadruple, even quintuple integral examples available on the net. There is no end to the order of integrals, as there is in theory no end to the number of dimensions one can mathematically describe (physically there may be, but then again string / loop theory seems to have come up with quite a few)...

I would like to see the integral program enhanced to do N-order integrals, and would suggest the following quintuple integral be used as a test (since it has been discussed at http://mathfaculty.fullerton.edu/mathews...nk_15.html and they suggest several methods for the solution...

With f(x,y,z,u,w) = sqrt(6-x^2-y^2-z^2-u^2-w^2) evaluate
integ(0,0.7) [ integ(0,0.8) [ integ(0,0.9) [ integ(0,1.0) [ integ(0,1.1) f(x,y,z,u,w) dw ]
du ] dz ] dy ] dx. The answer seems to lie around 1.189.

Greg