Application of ...

The area of the triangle formed by the positive X-axis and the normal and tangent to the circle $$x^{2}+y^{2}=4$$ at $$(1,\sqrt{3})$$ in sq. units is:

I : The area bounded by $$ x=2\cos\theta,\  y=3\sin\theta$$ is $$ 36\pi$$ sq. units.
II: The area bounded by $$ x=2\cos\theta,\  y=2\sin\theta$$ is $$ 4\pi$$ sq.units.
Which of the above statement is correct?

The area between the curves $$y=\tan x$$,$$y=\cot x$$ and $$\mathrm{x}$$-axis $$(0\displaystyle \leq x\leq\frac{\pi}{2})$$ is

I: The area bounded by the line $$\mathrm{y}=\mathrm{x}$$ and the curve $$y=x^{3}$$ is $$1/_{2}$$ sq. units.
II: The area bounded by the curves $$y=x^{3}$$ and $$ y=x^{2}$$and the ordinates $$x=1$$, $$x=2$$ is $$\frac{7}{12}$$ sq. units.
Which of the above statement is correct?

Assertion(A): The area bounded by $$y^{2}=4x$$ and $$y=x$$ is $$\displaystyle \frac{8}{3}$$ sq. units.

Reason(R): The area bounded by $$y^{2}=4ax$$ and $$y=mx$$ is $$\displaystyle \frac{8a^{2}}{3m^{3}}$$ sq. units.

Area bounded by $$\displaystyle \mathrm{f}(\mathrm{x})=\max.(\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{x},\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{x})$$ $$\displaystyle \forall 0\leq x\leq\frac{\pi}{2}$$ and the co-ordinate axis is equal to:

The area lying in the first quadrant between the curves $$x^{2}+y^{2}=\pi^{2}$$ and $$y=\sin x$$ and y- axis is

The area of the portion of the circle $$x^{2}+y^{2}=1$$, which lies inside the parabola $${y}^{2}=1-x$$ is

Area of the region bounded by $$y=e^{x},y=e^{-x},x=0$$ and $$x=1$$ in sq. units is:

The area of the region bounded by the curves $$\mathrm{y}=\sqrt{x}$$ and $$y=\sqrt{4-3x}$$ and $$\mathrm{y}=0$$ is: