Answer
The region is bounded by the line $y=1$, the y-axis and y=\sqrt x$.
Work Step by Step
Case 1: The side from $(0,0)$ to $(0,1)$.
Then,we have $u=0; v=t$ where $0 \leq t \leq 1$
Now, under the transformation $x=u^2, y=v$, the parametric equations are
$x=0,y=t$ ; $0 \leq t \leq 1$
Case 2: The side from $(0,1)$ to $(1,1)$.
Then, we have $u=t; v=1$ where $0 \leq t \leq 1$
Now, under the transformation $x=u^2, y=v$, the parametric equations are: $x=t^2,y=1$ ; $0 \leq t \leq 1$
Case 3: The side from $(1,1)$ to $(0,0)$.
Then, we have $u=1-t; v=1-t$ where $0 \leq t \leq 1$
Now, under the transformation $x=u^2, y=v$, the parametric equations are: $x=(1-t)^2,y=1-t$ ; $0 \leq t \leq 1$
This gives: $x=y^2$
or, $y=\sqrt x$
Hence, the region is bounded by the line $y=1$, the y-axis and y=\sqrt x$.
