The area enclosed between the curves $$y = a{x^2}$$ and
$$x = a{y^2}\left( {a > 0} \right)$$ is $$1$$ sq. unit, then the value of $$a$$ is

The area bounded by the curves $$y = \sqrt x ,2y + 3 = x$$ and
$$x$$-axis in the 1^st quadrant is

The area bounded by the curves $$y = \left| x \right| - 1$$ and $$y = - \left| x \right| + 1$$ is

Let $$f\left( x \right) = \int\limits_1^x {\sqrt {2 - {t^2}} \,dt.} $$ Then the real roots of the equation
$${x^2} - f'\left( x \right) = 0$$ are