plot(data,char,size,clr)

968ba8b6-819c-4cb5-9b7a-9c8f0d6f7e21 10 3 5 decimal

&[DATE] &[TIME] - &[FILENAME]

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 31 line for data r3 r4 r5 augment 21 line :

Region boundaries x R x a 2 x - : x b x : x c 4 x - : x d x 2^4 - sqrt : 41 sys :

X x a x b ≡ x solve x b x c ≡ x solve x c x d ≡ x solve x d x a ≡ x solve 41 mat : 12 2.5 241 mat

XY X X 1 el R 1 el X 2 el R 2 el X 3 el R 3 el X 4 el R 4 el 41 mat augment (: 1122 2.5 1.5 2042 mat

x R XY . 14 black plot 2 1 sys

input integrand x y f x y + (2^:

I_1 x y f y 2 x - x int x 12 int : acc 100 I_2 x y f y x d 4 x - int x 2 2.5 int : 13 mat

I_1 I_2 I_1 I_2 + 31 mat 7.333 4.667 1231 mat

'N' random in critical region N 1000 :

Filling a critical region

size/define critical region.
Plot first before filling xmin 1 : xmax 2.5 : ymin 0 : ymax 2 : 22 mat space_x xmax xmin - (: space_y ymax ymin - (: 21 line 21 sys

A function that tests an arbitrary point 
for its membership in the critical region. x y Test x a y < (x b y > (* x c y > (* x d y < x 2 ≥ 1 cases * :

Coord XY . 14 black plot :

==================================

t0 1 time :

A routine that finds an array of N random 
pairs in the critical region. Pts i 1 N range x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 1 x y Test - x 1 Random space_x * xmin + 1 el : y 1 Random space_y * ymin + 1 el : 21 line while P i 1 el x : P i 2 el y : 51 line for P 21 line :

Fill Pts . 6 #808080 plot :

1 time t0 - 10 s *

x R Fill Coord 3 1 sys

solved coords 1122 2.5 1.5 2042 mat Area 1241 mat

2 x - x 4 x - 4 - x 2^+ sqrt 41 sys

x R Fill Coord 31 sys

Scale(M,Low,High)

M Low High Scale High Low - (M M Min - M Max M Min - 106 -^+ / (* Low + :

data spec pts i 1 data rows range p i el a b c spec : for v p 1 el : Unest 'p' j 2 p rows range v v p j el stack : for data v augment 51 line :

N 1000 :

xRnd N 1100 Random.N : yRnd N 1100 Random.N : zRnd N 1100 Random.N : 31 line

X xRnd 1 2.5 Scale : Y yRnd 02 Scale : Z zRnd 016 Scale : 31 line

input integrand x y f x y + (2^:

The region of interest falls entirely within the rectangle defined by ... 1 ≤ x ≤2.5 and 0 ≤ y ≤2

Bolean factor, NOT used Bol 2.5 1 - (20 - (* 160 - (* : 48

kount(x,y,z): the scalar Bolean counting function Monte Carlo integration x y z kount x a y < (x b y > (x c y > (* * z x y f < (* x d y < x 2 ≥ 1 cases * :

Monte Carlo double integration I 2.5 1 - (20 - (* 160 - (* 1 N / (* X n el Y n el Z n el kount n 1 N sum * : 11.568

I_1 x y f y 2 x - x int x 12 int : acc 100 I_2 x y f y x d 4 x - int x 2 2.5 int : 13 mat

I_1 I_2 I_1 I_2 + 31 mat 7.333 4.667 1231 mat