Answer
Diverges
Work Step by Step
Re-write as: $\lim\limits_{a \to \infty} \int_2^\infty \dfrac{dv}{\sqrt {v-1}}=\lim\limits_{a \to \infty} [2 \sqrt {v-1}]_2^a$
or, $=\lim\limits_{a \to \infty} [2 \sqrt {a-1}-2]$
or, $=\infty$
Thus, the limit does not exist, so the integral diverges.
