Please Help me with this integral

cristinelM

New member
Joined
Dec 19, 2011
Messages
3
Hello.I have a little problem with applying a Monte Carlo method : Importance Sampling.I need to calculate :
\(\displaystyle \int_{0}^{\infty}\int_{0}^{\infty}\frac{1}{2\pi\sqrt{(1+x^{2}+y^{2})^{3}}}dxdy\)
Can somebody help me ? Thanks in advance.

 
Hello.I have a little problem with applying a Monte Carlo method : Importance Sampling.I need to calculate :
\(\displaystyle \int_{0}^{\infty}\int_{0}^{\infty}\frac{1}{2\pi\sqrt{(1+x^{2}+y^{2})^{3}}}dxdy\)
Can somebody help me ? Thanks in advance.


try converting to polar co-ordinate

\(\displaystyle x \ = r * cos(\theta)\)

\(\displaystyle y \ = r * sin(\theta)\)

then

\(\displaystyle \int_{0}^{\infty}\int_{0}^{\infty}\frac{1}{2\pi\sqrt{(1+x^{2}+y^{2})^{3}}}dxdy\)

\(\displaystyle = \ \int_{0}^{\infty}\frac{r \cdot dr}{\sqrt{(1+r^{2})^{3}}}\)
 
try converting to polar co-ordinate

\(\displaystyle x \ = r * cos(\theta)\)

\(\displaystyle y \ = r * sin(\theta)\)

then

\(\displaystyle \int_{0}^{\infty}\int_{0}^{\infty}\frac{1}{2\pi\sqrt{(1+x^{2}+y^{2})^{3}}}dxdy\)

\(\displaystyle = \ \int_{0}^{\infty}\frac{r \cdot dr}{\sqrt{(1+r^{2})^{3}}}\)

Thanks for your help it was very usefull for me.
 
Top