1) Integration of Gaussian Distribution with $(x,y,z)$ ranging from $-\infty$ to $\infty$ 
gives 1 as expected using this command in mathematica. (Total Probability = 1)

$\sigma = 200000$ and $\mu=1000000$

```
Integrate[(E^(-(x - 1000000)^2/(2*200000^2))*E^(-(y - 1000000)^2/(2*200000^2))*
          E^(-(z -1000000)^2/(2*200000^2))/(200000*Sqrt[2*Pi])^3) , {x, -Infinity, Infinity}, 
          {y, -Infinity,    Infinity}, {z, -Infinity, Infinity}]

```

2) Now I want to integrate over $(x,y,z)$ such that $$\frac{x}{1+0.1}+\frac{y}{(1+0.1)^2}+\frac{z}{(1+0.1)^3}\geq 2000000 $$ given that $$x,y,z\geq0$$
So I wrote this in mathematica:

```
Integrate[(E^(-(x - 1000000)^2/(2*200000^2))*E^(-(y - 1000000)^2/(2*200000^2))
       *E^(-(z -1000000)^2/(2*200000^2))/(200000*Sqrt[2*Pi])^3) Boole[x/(1 + 0.1) + y/(1 + 0.1)^2
         + z/(1+ 0.1)^3 - 2000000 >= 0], {x, 0,   Infinity}, {y, 0, Infinity}, {z, 0, Infinity}]

```

But the answer I am getting is some very big number ($1.7\times10^{17}$)

Can anyone point out the mistake?