Find a piecewise smooth parametrization of the path C given in the following graph.
$r(t) = \begin{cases} t \hat{i} + 2tj, & 0 \le t \le 1\\ (2 - t)\hat{i} + 2\hat{j}, & 1 \le t \le 2\\ (4 - t)\hat{j}, & 2 \le t \le 4 \end{cases}$
$r(t) = \begin{cases} t \hat{i} + 2tj, & 0 \le t \le 1\\ (2 + t^2 - 2)\hat{i} - 2\hat{j}, & 1 \le t \le 2\\ (4 - t^2)\hat{j}, & 2 \le t \le 6 \end{cases}$