The area bounded by the curve $y = k \sin x$ between $x = \pi$ and $x = 2\pi$ is:

$A$ quadratic polynomial $y = f(x)$ with absolute term $3$ neither touches nor intersects the abscissa axis and is symmetric about the line $x = 1$. The coefficient of the leading term of the polynomial is unity. $A$ point $A(x_1, y_1)$ with abscissa $x_1 = 1$ and a point $B(x_2, y_2)$ with ordinate $y_2 = 11$ are given in a Cartesian rectangular system of coordinates $OXY$ in the first quadrant on the curve $y = f(x)$,where $O$ is the origin. The area bounded by the curve $y = f(x)$ and the line $y = 3$ is: (in $/3$)

The area of the region bounded by the curve $y = -2\sqrt{x}$ and the lines $x = 0$,$x = 1$,and $y = 0$ is . . . . . . sq. units.

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

The area (in sq. units) bounded by the curves $y=(x+1)^2, y=(x-1)^2$ and the line $y=\frac{1}{4}$ is

The area of the smaller region bounded by the circle $x^2 + y^2 = 4$ and the line $x = 1$ is...