How to use monte carlo method : importance sampling ?

[cristinelm]

Hello.I have a little problem with applying a Monte Carlo method : Importance Sampling.I need to calculate :

integral(0 to infinity) integral(0 to infinity) 1/(2 * pi * sqrt((1 + x^2 + y^2)^3))dxdy

Can somebody help me ? Thanks in advance.

 

[NascentOxygen]

Hello.I have a little problem with applying a Monte Carlo method : Importance Sampling.I need to calculate :

integral(0 to infinity) integral(0 to infinity) 1/(2 * pi * sqrt((1 + x^2 + y^2)^3))dxdy

Can somebody help me ? Thanks in advance.

Is this just a thought experiment, or have you booked computer time to actually carry it out?

Start by looking at the 3D shape whose volume you are wanting to estimate. Also, the result at the very foot of this wolfram alpha presentation seems almost the answer you should be aiming towards.

Monte Carlo integration in 2D is easy to grasp, along with the concept of Importance Sampling. I think I can see how it would apply to 3D.