Use the Change of Variables $x = \sqrt { 2 } u - \sqrt { \frac { 2 } { 3 } } v$

Short Answer

Use the change of variables $x = \sqrt { 2 } u - \sqrt { \frac { 2 } { 3 } } v$ , $y = \sqrt { 2 } u + \sqrt { \frac { 2 } { 3 } } v$ to evaluate $\iint _ { R } \left( x ^ { 2 } - x y + y ^ { 2 } \right) d A$ , where R is the region bounded by the ellipse $x ^ { 2 } - x y + y ^ { 2 } = 2$ .