Find probability function, find constant a

Question

$$f(x) = \begin{cases} \frac{2}{x^2} & |x| > a\\ 0 & |x|\leqslant a \end{cases}$$ How to find a ? I tried to integrate on intervals $(-a,0)$, $(0,a)$, but it equals $0$.

Answer 1

Hint: $1= \int_{-\infty}^{\infty} f(x)dx = \int_{-\infty}^{-a} \frac{2}{x^2} dx + \int_{a}^{\infty} \frac{2}{x^2} dx = 2*\int_{a}^{\infty} \frac{2}{x^2} dx = \frac{4}{a}.$