Originally Posted by

**MrSplashypants1** Alright, so we define

$\displaystyle g: D^* \longrightarrow D$

$\displaystyle (u,v) \longmapsto (x,y)$

where u=x+2y and v=3x-y

Then $\displaystyle D^*$ is the square region bounded by $\displaystyle 0 \leq u \leq (\pi/2) and 0\leq v \leq (\pi/2)$

And so the original integral becomes $\displaystyle \int_0^\frac{\pi}{2}\int_0^\frac{\pi}{2}sin(u)sin( v)|detJ_{g} (u,v)|dudv$

where the determinant = $\displaystyle \frac{1}{7}$

and so the integral comes out as just $\displaystyle \frac{1}{7}$ as well?