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

$AOB$ is the positive quadrant of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ in which $OA=5, OB=3$. The area between the arc $AB$ and the chord $AB$ of the ellipse in sq. units is

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

The area bounded by the curve $y = x^2 + 2$,the $x$-axis,and the lines $x = 1$ and $x = 2$ is:

Let the straight line $x=b$ divide the area enclosed by $y=(1-x)^2, y=0$,and $x=0$ into two parts $R_1(0 \leq x \leq b)$ and $R_2(b \leq x \leq 1)$ such that $R_1-R_2=\frac{1}{4}$. Then $b$ equals

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