HP-41 Challenge: Double Integrals by INTEG Recursion

[Valentin Albillo]

(05-31-2016 04:52 PM)gjmcclure Wrote:  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.

This quintuple integral is easy as pie for the HP-71B w/Math ROM using straight out-of-the-box code with no fancy programming or buffer juggling needed.

Assorted results for increasing precision (1E-1, 1E-2, ..., 1E-5) are as follows:

>LIST

10 DEF FNF(X,Y,Z,U,W)=SQR(6-X*X-Y*Y-Z*Z-U*U-W*W)
20 DEF FNG(X,Y,Z,U)=INTEGRAL(0,1.1,K,FNF(X,Y,Z,U,IVAR))
30 DEF FNH(X,Y,Z)=INTEGRAL(0,1,K,FNG(X,Y,Z,IVAR))
40 DEF FNI(X,Y)=INTEGRAL(0,.9,K,FNH(X,Y,IVAR))
50 DEF FNJ(X)=INTEGRAL(0,.8,K,FNI(X,IVAR))

60 FOR I=1 TO 5 @ K=1/10^I @ DISP K,INTEGRAL(0,.7,K,FNJ(IVAR)) @ NEXT I

>DESTROY ALL
>RUN

.1 1.18887862667
.01 1.18887862667
.001 1.18882510429
.0001 1.18878513051
.00001 1.18878333625

so we get from 5 to 8 correct digits give or take a couple ulps, as compared to Mathematica's 1.18878359.

Regards.
V.
.