Answer
The region is bounded by the line $y=1$, the y-axis and $y=\sqrt x$.
Work Step by Step
We are given that the triangular region with vertices $(0,0), (0,1), (1,1)$.
a) Let us consider the case with the side from $(0,0)$ to $(0,1)$.
Then, $u=0; v=t$ where $0 \leq t \leq 1$
Under the transformation $x=u^2, y=v$, we have parametric equations as: $x=0,y=t$ where $0 \leq t \leq 1$
b) Let us consider the case when the side from $(0,1)$ to $(1,1)$.
Then, $u=t; v=1$ where $0 \leq t \leq 1$
Under the transformation $x=u^2, y=v$, we have parametric equations as: $x=t^2,y=1$ where $0 \leq t \leq 1$
c) Let us consider the case with the side from $(1,1)$ to $(0,0)$.
Then, $u=1-t; v=1-t$ where $0 \leq t \leq 1$
Under the transformation $x=u^2, y=v$, we have parametric equations as: $x=(1-t)^2,y=1-t$ where $0 \leq t \leq 1$
Thus, $x=y^2 \implies y=\sqrt x$
Hence, the region is bounded by the line $y=1$, the y-axis and $y=\sqrt x$.
