Difficult# Change of Variable According to Integrand and Boundary

MVCALC-UQZEYZ

Evaluate the following double integral using a change of variables:

$$I=\iint_R (x-2y)\sqrt{x-3y}dA$$

...where $R$ is the triangular region $R$ bounded by $x-2y=1$, $x-3y=0$ and $y=0$.