The area of the region bounded by $y=||x-3|-4|-5$ and the $X$-axis is

The area of the region bounded by the curve $y = 2 - x - 3x^2$, the $X$-axis, the $Y$-axis, and the line $x = -2$ is

The area bounded by the curve $y = \log x$,the $x$-axis,and the ordinates $x = 1$ and $x = 2$ 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?

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

If the ordinate $x = a$ divides the area bounded by the curve $y = \left( 1 + \frac{8}{x^2} \right)$,the $x$-axis,and the ordinates $x = 2$ and $x = 4$ into two equal parts,then $a = $