The area of the region bounded by the curve $y = \cot x$,the lines $x = \frac{\pi}{4}$,$x = \frac{\pi}{2}$,and the $X$-axis is . . . . . . sq. units.

The area of the region bounded by the curve $y=x|x|$,lines $x=-1$ and $x=1$ is . . . . . . .

The area bounded by the curves $x = \sqrt{2 - y^2}$ and $|x| = |y|$ 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:

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 bounded by the curve $x=4-y^2$ and the $Y$-axis is