Examples: Find the area of the region bounded by the curve `y^2 = 2y - x` and the y-axis.

Explanation

`y^2=2y-x rArr y^2-2y+1 =-x+1`
`rArr (y-1)^2=-(x-1)`
So, the given equation represents a parabola that opens on the left, having vertex at (1,1) ,
Now , x`= 0 rArr y^2 - 2y rArr y^2 -2y =0 `
`rArr y(y-2) =0`
`rArr y(y-2)=0`
`y=0 or y=2`
Thus the curve meets the y-axis at (0,0) and (0,2)
Required area `=underset(0)overset(2)int (2y-y^2)dy `