[VA] SRC #011 - April 1st, 2022 Bizarro Special

[Albert Chan]

Difference of two uniform distribution form triangular distribution.
This reduced sextuple to triple integral.

We just integrate ∫∫∫(f(x,y,z) dz dy dx), with all variables from 0 to 1

Let x = |x2-x1|, y = |y2-y1|, z = |z2-z1|, all with distribution ◣
Squaring is going to remove abs() anyway.

For x, we do need ◢◣ distribution, center at d, thus (d+x), (d-x) terms.
Because of the discontinuity at x=0, we fold the 2 integrals as 1.
This moved the discontinuity to the edge.

Here is HP71B equivlent code (smaller P actually make things worse)

10 P=.01 @ D=1 @ T=TIME
20 DEF FNZ(X,Y)=INTEGRAL(0,1,P,X/(X*X+Y*Y+(1-SQR(IVAR))^2)^1.5)
30 DEF FNY(X)=INTEGRAL(0,1,P,FNZ(X,1-SQR(IVAR)))
40 DEF FNX(X)=FNY(D+X)+FNY(D-X)
50 DISP INTEGRAL(0,1,P,FNX(1-SQR(IVAR)))/2, IBOUND, TIME-T

>RUN
 .92596918938      1.84480545818E-2      21.66