Application of ...

Area of the region bounded by the curve $$y^{2}=4x, y-$$ axis and the line $$y=3$$ is 

I: The area bounded by the curves $$y=\sin x,\ y=\cos x$$ and $$\mathrm{Y}$$-axis is $$\sqrt{2}-1$$ sq. units.
II: The area bounded by $$y=\cos x,\ y=x+1,\ y=0$$ is 3/2 sq. units.

Which of the above statement is correct?

Arrangement of the following areas between the curves is descending order:
$$\mathrm{A}:y^{2}=4x,\ x^{2}=4y$$
$$ \mathrm{B}.\ y=x,\ y=x^{3}$$
$$\mathrm{C}.\ y^{2}=8x,y=2x$$
$$ \mathrm{D}.\ y=\sqrt{x},\ y=x^{2}$$

Match the following:

The area bounded by the $$y=\left| \sin { x }  \right| $$, x-axis and the lines $$\left| x \right| =\pi $$ is

Match the following:

The area of the region bounded by the curves $$y=ex\log x$$ and $$y=\displaystyle \frac{\log x}{ex}$$ is:

Area of the figure bounded by the lines $$ y=\sqrt{x},x\in [0,1],\ y=x^{2},\ x\in[1,2]$$ and $$y=-x^{2}+2x+4,x\in0,2]$$ is:

The area bounded by the parabolas $$\mathrm{y}^{2}=5\mathrm{x}+6$$ and $$\mathrm{x}^{2}=\mathrm{y}$$

The ratio of the areas into which the circle $$x^{2}+y^{2}=64$$ is divided by the parabola $$y^{2}=12x$$ is: