The area (in square units) bounded by the line $y = x$, the $X$-axis and the lines $x = -2$ and $x = 4$ is...

Consider a region $R=\{(x, y) \in \mathbb{R}^{2}: x^{2} \leq y \leq 2 x\}$. If a line $y=\alpha$ divides the area of region $R$ into two equal parts,then which of the following is true?

The value of $a$ $(a > 0)$ for which the area bounded by the curves $y = \frac{x}{6} + \frac{1}{x^2}$,$y = 0$,$x = a$ and $x = 2a$ has the least value,is

Consider the function $f(x) = x^3 - 8x^2 + 20x - 13$. The area enclosed by $y = f(x)$ and the coordinate axes is:

The area bounded by the curve $y^2 = 4ax$,the $x$-axis,and the ordinates $x = 0$ and $x = a$ is

Find the area of the parabola $y^{2}=4ax$ bounded by its latus rectum.