The area of the region bounded by the parabola $${\left( {y - 2} \right)^2} = x - 1,$$ the tangent of the parabola at the point $$(2, 3)$$ and the $$x$$-axis is :

The area of the plane region bounded by the curves $$x + 2{y^2} = 0$$ and $$\,x + 3{y^2} = 1$$ is equal to :

The area enclosed between the curves $${y^2} = x$$ and $$y = \left| x \right|$$ is :

The area enclosed between the curve $$y = {\log _e}\left( {x + e} \right)$$ and the coordinate axes is :