Please help me to sole the following..
$\displaystyle I=\int{\int{\ln\left(\frac{1}{\sqrt{x^2+y^2}} \right) dxdy$
Thank you very much..
The first thing you should do is use properties of logarithms to write the integrand as $\displaystyle ln\left(\frac{1}{\sqrt{x^2+ y^2}}\right)= -\frac{1}{2}ln(x^2+ y^2)$. then change to polar coordinates so that $\displaystyle x^2+ y^2= r^2$ and $\displaystyle dxdy= r drd\theta$. The integral become $\displaystyle -\frac{1}{2}\int\int ln(r^2)r dr\theta= -\frac{1}{2}\int d\theta \int ln(r^2) r dr$. Can you do that?