The graphs of sine and cosine functions intersect each other at a number of points,and between two consecutive points of intersection,the two graphs enclose the same area $A$. Then $A^{4}$ is equal to ............

The area of the region bounded by the parabola $y^2 = 8x$ and its latus rectum is . . . . . . sq. units.

$A$ 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 of the region bounded by the curve $y^2 = 4x$ and the line $x = 3$ is . . . . . . sq. units.

Find the area bounded by the curves $(x-1)^{2}+y^{2}=1$ and $x^{2}+y^{2}=1$.

The area of the region bounded by $y=||x-3|-4|-5$ and the $X$-axis is