Describe the Image R of the Set $S = \{ ( u , v ) \mid 0 \leq u \leq 1,0 \leq v \leq 1 \}$

Essay

Describe the image R of the set $S = \{ ( u , v ) \mid 0 \leq u \leq 1,0 \leq v \leq 1 \}$ under the transformation $x = 3 u + v$ , $y = u + 2 v$ , and then compute $\iint _ { R } \left( x y + y ^ { 2 } \right) d A$ .