Let y = f(x) be the function defined on -1 <= x <= 1 by the formula
\[y = \sqrt{4 - (x - 1)^2} - 1.\]
This is a graph of y = f(x):
If a graph of x = f(y) is overlaid on the graph above, then one fully enclosed region is formed by the two graphs. What is the area of that region, rounded to the nearest hundredth?
+605 $y=\sqrt{4-(x-1)^2}-1$
$(y+1)^2=4-(x-1)^2$
$(x-1)^2=4-(y+1)^2$
$x=1+\sqrt{4-(y+1)^2}$
Switch $x,y$ and get $y=1+\sqrt{4-(x+1)^2}$.
Graph and you will see magic.
