Area lying in the first quadrant and bounded by the ellipse $4x^2 + 9y^2 = 144$ is . . . . . . . (in $\pi$)

The area of the region bounded by the curve $y=9-x^2$,the $X$-axis,and the lines $x=0$ and $x=3$ is . . . . . . sq. units.

If the area bounded by the curve $y = x^3 + ax$ (where $a > 0$), the $X$-axis, and the lines $x = -2$ and $x = 1$ is $\frac{37}{4} \text{ square units}$, find the value of $a$.

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 parabola $y^2 = 27x$ and the line $x = 1$ is . . . . . . sq. units. (in $\sqrt{3}$)

If the area of the region enclosed by the curve $x^2+y^2=16$ and the lines $x=2$ and $x=3$ is $\left(3 \sqrt{7}-4 \sqrt{3}-\frac{8 \pi}{3}+k\right)$ sq units,then $k$ equals