9b2bc823-1455-4270-a1f7-4c9bb5c3208c 21 Valery Ochkov 4 5 false false false 0 3 decimal

Some old SMath version can calculate this, but not anymore:

x 2^y 2^+ 1 - (3^x 2^y 3^* - 0 ≤ x 1.5 - 1.5 int y 1.5 - 1.5 int

Heart:

x y f x m / (2^y m / (2^+ 1 - (3^x m / (2^y m / (3^* - :

Monte Carlo:

a b rnd a b a - (109 -^* 109^random * + :

x y f a b c d Nx Ny ∫.MC a b rnd c d rnd f 0 ≤ n 1 Ny sum m 1 Nx sum (b a - Nx / * d c - Ny / * :

S.♡ x y f 1.5 m * - 1.5 m * 1.5 m * - 1.5 m * 100100 ∫.MC : 3.1446 m 2^*

With animation

N 100 :

k 1 N range :

X k el 1.5 m * - 1.5 m * rnd eval :

Y k el 1.5 m * - 1.5 m * rnd eval :

F X Y f vectorize :

S k el 32^k / F j el 0 ≤ (j 1 k sum (* :

M X Y . 4 red F 0 ≤ blue cases vectorize augment :

I 1.2 - 1 - S 4 var2str vectorize augment :

x m * y m * f M 1 k range 1 5 range el I k 1 3 range el 3 1 sys

S N el 3.06

Discretizing:

a 1.5 m * - :

b 1.5 m * :

N 100 :

k 1 N range :

ΔX b a - N / :

X k el a k 0.5 - (ΔX * + :

ΔY b a - N / :

Y k el a k 0.5 - (ΔY * + :

S.♡ X m el Y n el f 0 ≤ n 1 N sum m 1 N sum (ΔX ΔY * * : 3.6612 m 2^*

Solving for y:

x φ 44 x 2^* - x 43 /^+ :

x.max x φ x 1 roots : 1.139

S.♡ 2 x φ abs sqrt x 0 x.max int * m 2^* : 3.6618 m 2^*

Alvaro

4 appVersion 1.75.9678.0