Determine if the improper integral is convergent or divergent, and find its value if it is convergent.
\int_{2}^{\infty} \frac{1}{6x^{2}} dx
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The improper integral is convergent and \int_{2}^{\infty} \frac{-1}{6x^{2}} dx = -\frac{1}{12}.
(Type an integer or a fraction. Simplify your answer.)
B. The improper integral diverges.
