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

Let $A$ be the area bounded by the curve $y = \cos^{-1}\sqrt{1 - x^2}$,the tangent to the curve $y = \sin^{-1}x$ at $x = 0$,and the line $x = 1$. Then the value of $2(\{A\} + \text{sgn}(A))$ is (where $\{.\}$ is the fractional part function and $\text{sgn}(x)$ is the signum function).

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

The area under the curve $y = |\cos x - \sin x|$,$0 \leq x \leq \frac{\pi}{2}$,and above the $x$-axis is

The area (in sq. units) of the region bounded by the curves $y = 2^x$ and $y = |x + 1|$ in the first quadrant is

The area of the region bounded by the curve $y^2 = 4x$,the $Y$-axis,and the line $y = 3$ is . . . . . . sq. units.