The area of the region enclosed between the parabola $y^{2}=x$ and the line $y=mx$ is $\frac{1}{48}$. Then, the value of $m$ is

The area of the region bounded by the curves $y=x^{2}$ and $x=y^{2}$ is

The area of the region bounded by the curve $x+2y=8$,the $X$-axis,and the lines $x=1$ and $x=5$ using integration is . . . . . . sq. units.

The area enclosed by the curve $y = (x - 1)(x - 2)(x - 3)$ between the coordinate axes and the ordinate at $x = 3$ is:

If $S$ be the area of the region enclosed by $y=e^{-x^2}, y=0, x=0$,and $x=1$. Then
$(A) S \geq \frac{1}{e}$
$(B) S \geq 1-\frac{1}{e}$
$(C) S \leq \frac{1}{4}\left(1+\frac{1}{\sqrt{e}}\right)$
$(D) S \leq \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{e}}\left(1-\frac{1}{\sqrt{2}}\right)$

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