The measurement of the area bounded by the coordinate axes and the curve $y = \log_e x$ is

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

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

The area of the region enclosed by the curves $y=e^x$,$y=|e^x-1|$ and the $y$-axis is:

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

The area of the region bounded by the curve $y=x^3$, its tangent at $(1,1)$, and the $X$-axis is