Given

${}_R{x}^2-xy{y}^{2}dA$

Evaluate the given integral where R is the ellipse given by $x^2-xy{y}^{2}2$ using the following transformation,

$x=\sqrt[\phantom{2}]{2}u-\sqrt[\phantom{2}]{\frac{2}{3}}v,y=\sqrt[\phantom{2}]{2}u\sqrt[\phantom{2}]{\frac{2}{3}}v$

$(6$ pts$.)$