$(1$ point$)$ Consider the region $R$ in the $xy-$plane that is described by the intersection of the four lines:

$2x-4y=2$

$2x-4y=4$

$2x+5y=3$

$2x+5y=4$

Use the transformation $T$ described by $u=2x-4y$ and $v=2x+5y$ to evaluate the following double integral:

${}_R(2x-4y)\sqrt[\phantom{2}]{2x+5y}dxdy=$

$$