The area (in square units) of the region bounded by the curve $y^2 = 4ax\ (a > 0)$ and the lines $y = 2a, x = 0$ is equal to:

The area (in sq. units) of region bounded by the curves $y^2 = 4x$ and $y = x$ is:

The area (in sq. units) bounded by the curve $y = \cos x$ and x-axis between $x = 0$ and $x = \frac{3\pi}{2}$ is

The area (in sq. units) of the region $\{(x,y): 3x^2 \leq y \leq |x|\}$ is equal to

Area bounded by the curves

$y=\begin{cases}x+2, & x\ge-1\\-x, & x<-1\end{cases}$, $x=-2, x=3$ and $y=0$ is:

Evaluate $\int_0^{\frac{1}{3}} y \, dx$

The area bounded by an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and the lines $x=0, x=ae$ and the $x$-axis in the first quadrant, where $e$ is the eccentricity of the ellipse, is: