The solution for $x$ of the equation $\begin{align*}\int_{\sqrt{2}}^x \; \; \frac{dt}{t \sqrt{t^2 -1}} = \frac{\pi}{2} \end{align*}$ is :

Question

( A ) $2$
( B ) $\sqrt{3} / 2$
( C ) $2 \sqrt{2}$
( D ) $-\sqrt{2}$