Application of ...

The area of the region bounded by the parabola $$(\mathrm{y}-2)^{2}=\mathrm{x}-1$$, the tangent to the parabola at the point $$(2,\ 3)$$ and the $$\mathrm{x}$$-axis is 

The area (in square units) of the region bounded by the curves $$y + 2x^2 = 0$$ and $$y + 3x^2 = 1$$, is equal to 

The area (in sq. units) of the region $$\{(x, y):x \geq 0, x+y \leq 3, x^2 \leq 4y$$ and $$y\leq 1+\sqrt{x}\}$$ is.

The area of the region described by $$ A= (x,y):x^{2}+y^{2}\leq 1$$ and $$ y^{2}\leq 1-x$$ is:

The parabolas $$y^{2}=4x$$ and $$x^{2}=4y$$ divide the square region bounded by the lines x = 4, y = 4 and the coordinate axes. If $$S_{1},S_{2},S_{3}$$ are respectively the areas of these parts numbered from top to bottom(Example: $$S_1$$ is the area bounded by $$y=4$$ and $$x^{2}=4y$$ ); then $$S_{1},S_{2},S_{3}$$ is  

The area of the region bounded by the curves $$x+2y^{2}=0$$ and $$x+3y^{2}=1$$ is equal to 

 The area bounded by the curves $$\mathrm{y}=$$ cosx and $$\mathrm{y}=$$ sinx between the ordinates $$\mathrm{x}=0$$ and $$\displaystyle \mathrm{x}=\frac{3\pi}{2}$$:

The area (in square units) bounded by the curves $$y=\sqrt{x},\ 2y-x+3=0$$, $$X-$$axis, and lying in the first quadrant is:

The area bounded between the parabolas $$4 x^{2}=y$$ and $$x^{2}=9y$$, and the straight line $$\mathrm{y}=2$$ is:

The area (in sq. units) of the region $$\left\{ \left( x,y \right) \in { R }^{ 2 }:{ x }^{ 2 }\le y\le 3-2x \right\} $$, is: