Area enclosed by the ellipse $9x^2 + 4y^2 = 1$ in the first quadrant is . . . . . . .

The area bounded by the line $y=x$,the $x$-axis,and the ordinates $x=-1$ and $x=2$ 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:

The area of the region bounded by the curve $y=\log x$,the $x$-axis,and the lines $x=1, x=e$ is

The area in square units of the region bounded by the curve $y = \sqrt{16 - x^2}$ and the lines $x = 0, x = 4$ above the $X$-axis is: (in $\pi$)

The area of the region bounded by the curve $y = x^2 - x - 6$,the $x$-axis $(y = 0)$,and the lines $x = -1$ and $x = 1$ is . . . . . . sq. units.