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

The area (in square units) of the region bounded by the circle $x^2 + y^2 = 9$ and the parabola $y^2 \leq 8x$ is...

If the area of the region bounded by the parabola $y^2 = 4kx$ and the line $x = k$, (where $k > 0$) is $\dfrac{128}{3}$ sq. units, then the value of $\sin^{-1}\left(\dfrac{2}{k}\right)$ is equal to...

The area (in sq. units) of the region enclosed by $\{(x, y) \mid y \leq x^2, xy \leq 8, y \geq 1\}$ is...