Area of the region bounded by the curve $|x| + y = 1$ is . . . . . . sq. units.

The area bounded by the curve $y=\sin^{2} x$,the $x$-axis,and the lines $x=0$ and $x=\frac{\pi}{2}$ is

The area bounded by $y=x^{3}$,$y=8$,and $x=0$ is

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:

$A$ farmer $F_1$ has a land in the shape of a triangle with vertices at $P(0,0)$,$Q(1,1)$,and $R(2,0)$. From this land,a neighbouring farmer $F_2$ takes away the region which lies between the side $PQ$ and a curve of the form $y = x^n$ $(n > 1)$. If the area of the region taken away by the farmer $F_2$ is exactly $30\%$ of the area of $\triangle PQR$,then the value of $n$ is:

Area of the region bounded by the curve $y=x|x|$,$X$-axis and lines $x=0$ and $x=1$ is . . . . . . sq. units.