The area bounded between the parabola $y^{2}=4x$ and the line $y=2x-4$ is equal to

The area of the region under the curve $y=|\sin x-\cos x|$,$0 \leq x \leq \frac{\pi}{2}$ and above the $x$-axis,is (in square units)

The area of the region bounded by the curve $y=x^{2}+1$,the lines $x=1, x=2$ and the $X$-axis is

The area enclosed between the curves $y=x|x|$ and $y=x-|x|$ 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 (in square units) of the region bounded by $x^2=8y$, $x=4$ and the $X$-axis is: