Crude Monte Carlo quadrature in infinite variance case and the Central Limit Theorem

After a short discussion of Monte Carlo integration the crude Monte Carlo method is tested by estimating the integrals

$$\int\limits_0^1 {\left( {\frac{1}{x}} \right)^{1/v} } dxas\bar f_n = \frac{1}{n}\sum\limits_{i = 1}^n {\left( {\frac{1}{{\xi _i }}} \right)^{1/v} ,} $$