The area of the region bounded by the curve $y = x|x|$,the $x-$axis,and the ordinates $x = 1$ and $x = -1$ is given by:

The area (in sq unit) of the region bounded by the curves $2x = y^2 - 1$ and $x = 0$ is

Area of the region bounded by the curve $y=\cos x$,$x=\frac{\pi}{2}$ and $x=\frac{3 \pi}{2}$ is . . . . . . sq. units.

The area of the region bounded by the curves $y = |x - 4|$, $x = 3$, $x = 5$, and 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 $y=e^x$ and lines $x=0$ and $y=e$ is