The area bounded by the curve $y=x^3-3x^2+2x$ and the $X$-axis is (in square units)

Area of the region bounded by the curve $y = x^3$, $x$-axis and the ordinates $x = -1$ and $x = 2$ is . . . . . . . (in $/4$)

If the area of the region $\{(x, y): -1 \leq x \leq 1, 0 \leq y \leq a + e^{|x|} - e^{-x}, a > 0\}$ is $\frac{e^2 + 8e + 1}{e}$,then the value of $a$ is:

The area (in sq unit) of the region bounded by the curves $2x = y^2 - 1$ and $x = 0$ is

If the area bounded by the parabola $y^2=16ax$ and the line $y=4mx$ is $\frac{a^2}{12}$ sq. units,then the value of '$m$' is

Let $A$ be the area bounded by the curve $y = \cos^{-1}\sqrt{1 - x^2}$,the tangent to the curve $y = \sin^{-1}x$ at $x = 0$,and the line $x = 1$. Then the value of $2(\{A\} + \text{sgn}(A))$ is (where $\{.\}$ is the fractional part function and $\text{sgn}(x)$ is the signum function).