Evaluate the surface integral $\displaystyle \int\!\int_H 6 y \, dA$ where $H$ is the helicoid (i.e., spiral ramp) given by the vector parametric equation

$$\boldsymbol{\vec{r}} \left( u, v \right) = \langle u \cos v, u \sin v, v \rangle, \ \ \ 0 \leq u \leq 1, \ \ \ 0 \leq v \leq 3 \pi.$$

$\displaystyle \int\!\int_H 6 y \, dA =$