Area of the region bounded by the curve $y = x^3$, $x$-axis and the ordinates $x = -1$ and $x = 2$ is . . . . . . . (in $/4$)

$AOB$ 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 graphs of $f(x) = x^2$ and $g(x) = cx^3$ (where $c > 0$) intersect at the points $(0, 0)$ and $\left( \frac{1}{c}, \frac{1}{c^2} \right)$. If the area of the region lying between these graphs over the interval $[0, 1/c]$ is equal to $2/3$,then the value of $c$ is:

Area of the region bounded by $y = \cos x$,$x = -\frac{\pi}{2}$ and $x = \frac{\pi}{2}$ is . . . . . . .

The area bounded by the curve $y = x \sin x$ and the $x$-axis between $x = 0$ and $x = 2\pi$ is:

Area of the region bounded by the curve $y^{2}=4x$,$y$-axis and the line $y=3$ is