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 $y = 2^{kx}$ and the lines $x = 0$ and $x = 2$ in the first quadrant is $\frac{2}{\log_e 2}$. Find the value of $k$.

The area bounded by the curve $y = f(x)$,$x-$ axis and ordinates $x = 1$ and $x = b$ is $(b - 1)\sin(3b + 4)$. Then $f(x)$ is:

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

Find the area of the region in the first quadrant enclosed by the $x-$ axis,the line $x=\sqrt{3} y$ and the circle $x^{2}+y^{2}=4$.

Let $f(\alpha)$ denote the area of the region in the first quadrant bounded by $x=0, x=1, y^{2}=x$ and $y=|\alpha x-5|-|1-\alpha x|+\alpha x^{2}$. Then $f(0)+f(1)$ is equal to