The area of the smaller portion between the curves $x^2 + y^2 = 8$ and $y^2 = 2x$ is

The area bounded by the curves $y-1=\cos x$,$y=\sin x$ and the $X$-axis between $x=0$ and $x=\pi$ is

Let the area of the region bounded by the curve $y=\max\{\sin x, \cos x\}$,lines $x=0, x=\frac{3\pi}{2}$ and the x-axis be $A$. Then,$A+A^{2}$ is equal to:

The area (in sq. units) of the region $\{ (x,y) : x \ge 0, x + y \le 3, x^2 \le 4y \text{ and } y \le 1 + \sqrt{x} \}$ is:

The area of the region included between the parabola $y^{2}=x$ and the line $x+y=2$ in the first quadrant is

Let $A = \{(x, y) \in R^2 : y \geq 0, 2x \leq y \leq \sqrt{4-(x-1)^2}\}$ and $B = \{(x, y) \in R \times R : 0 \leq y \leq \min \{2x, \sqrt{4-(x-1)^2}\}\}$. Then the ratio of the area of $A$ to the area of $B$ is