Area bounded by the curve $$y = {x^2}$$ and the lines $$x=4$$ and $$y=0$$ is given by

If a function is continuous at a point its first derivative

The area bounded by the parabola $$2y = {x^2}$$ and the lines $$x=y-4$$ is equal to _________.

The value of $$\int\limits_0^\infty {{e^{ - {y^3}}}.{y^{1/2}}} $$ dy is _________.