Convert to cylindrical coordinates and evaluate:

${}_{E}z\sqrt[\phantom{2}]{x^2{y}^2}dV,E=\{(x,y,z)|x^2{y}^{2}4,0z3\}$

Use spherical coordinates to find the volume of:

$E=\{(x,y,z)|1x^2{y}^2{z}^{2}9,z0\}$

Let $u=2x-y,v=xy$

$($a$)$ Find the Jacobian $J(x,yu,v)$

$($b$)$ Find the inverse transformation

$($c$)$ Transform ${}_R$xydA where $R$ is the unit square with vertices $(0,0),(1,0),(1,1),(0,1)$

Evaluate ${}_R{e}^{\frac{y-x}{yx}}dA,$ where $R$ is the triangle with vertices $(0,0),(1,0),(0,1).$ Use substitution $u=y-x,v=yx$