The area of the region bounded by the curve $y = 2^{kx}$ and $x = 0, x = 2$, in first quadrant is $\dfrac{2}{\log 2}$, then the value of $k$ is

The area of the region bounded by the curve $y = x^3$ and the lines $y = 8$ and $x = 0$ is ... square units.

The area of the region (in sq.units) bounded by the curve $y = 2\sqrt{1 - x^2}$ and the X-axis is _____

The area bounded by the curve $y = x\left|\sin\left(\dfrac{x}{2}\right)\right|$ and the X-axis between the lines $x = 0$ and $x = 4\pi$ (in square units), is....