The area of the region $A = \{ (x,y) : 0 \le y \le x|x| + 1, -1 \le x \le 1 \}$ in square units is:

The line $x=\frac{\pi}{4}$ divides the area of the region bounded by $y=\sin x$, $y=\cos x$ and the $x$-axis $\left(0 \leq x \leq \frac{\pi}{2}\right)$ into two regions of areas $A_1$ and $A_2$. Then $A_1 : A_2$ equals (in $: 1$)

The ratio of the areas bounded by the curves $y = \cos x$ and $y = \cos 2x$ between $x = 0$ and $x = \frac{\pi}{3}$ with the $X$-axis is:

The area of the region bounded by the curve $y = \cos x$ between $x = 0$ and $x = \pi$ is

The area of the region bounded by the curve $y=4x^{3}-6x^{2}+4x+1$ and the lines $x=1, x=5$ and the $x$-axis is

The area (in $sq. \,units$) of the region,given by the set $\{(x, y) \in R \times R \mid x \geq 0, 2x^2 \leq y \leq 4-2x\}$ is: