The area enclosed by the ellipse $25x^2 + 16y^2 = 400$ is . . . . . . sq. units. (in $\pi$)

The area of the region bounded by the curve $y=4x^{3}-6x^{2}+4x+1$ and the lines $x=1, x=5$ and the $x$-axis is

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:

$A$ 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 bounded by the lines $y = 2 + x$,$y = 2 - x$,and $x = 2$ is

The area bounded by the parabola ${y^2} = 4ax$ and its latus rectum is: