Let $z=x+iy$ be a complex number $(x, y \in R)$. Let $A$ and $B$ be two sets such that $A=\{z:|z| \leq 2\}$ and $B=\{z:(z+2y)+\bar{z} \geq 4\}$. The area of region $A \cap B$ is

The area of the region bounded by the curve $y = 2x - x^2$ and the $X$-axis 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:

Find the area of the region bounded by the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$. (in $\pi$)

The area of the region bounded by the parabola $x^{2}=16y$,the lines $y=1$,$y=4$,and the $Y$-axis in the first quadrant is:

The area bounded by the curve $y = x^3$,the $x$-axis,and the ordinates $x = 1$ and $x = 4$ is: