If $ f(x) = \left\{ \begin{array}{l l} kx^{2}, & \quad \text{$0<x<3$}\\ 0, & \quad \text{elsewhere} \end{array} \right. $ is a probability density function then the value of $k$ is

Question

\[\begin{array}{1 1}(1)\frac{1}{3}&(2)\frac{1}{6}\\(3)\frac{1}{9}&(4)\frac{1}{12}\end{array}\]