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

The area of the region bounded by the curve $y=|x-2|$ between $x=1, x=3$ and the $X$-axis is ......

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.

For which of the following values of $m$,the area of the region bounded by the curve $y = x - x^2$ and the line $y = mx$ equals $\frac{9}{2}$?

The line $y = mx$ bisects the area enclosed by the curve $y = 1 + 4x - x^2$ and the lines $x = 0, x = \frac{3}{2}$ and $y = 0$. Then the value of $m$ is:

If the area of the region $\{(x, y): \frac{a}{x^2} \leq y \leq \frac{1}{x}, 1 \leq x \leq 2, 0 < a < 1\}$ is $(\log_e 2) - \frac{1}{7}$,then the value of $7a - 3$ is equal to: