Application of ...

Let $$S(\alpha) = \{ (x, y) : y^2 \le x, 0 \le x \le \alpha\}$$ and $$A(\alpha)$$ is area of the region $$S(\alpha)$$. If for a $$\lambda , 0 < \lambda < 4, A(\lambda) : A(4) = 2 : 5$$, then $$\lambda$$ equals

If the area (in sq. units) bounded by the parabola $$y^{2} = 4\lambda x$$ and the line $$y = \lambda x, \lambda > 0$$, is $$\dfrac {1}{9}$$, then $$\lambda$$ is equal to

The area (in sq. units) of the region bounded by the curves $$y={2}^{x}$$ and $$y=\left| x+1 \right| $$, in the first quadrant is:

Area of the region bounded by $$y^2\leq 4x, x+y\leq 1, x\geq 0, y\geq 0$$ is $$a\sqrt{2}+b$$, then value of $$a-b$$ is?

If the area enclosed by the curves $${ y }^{ 2 }=4\lambda x$$ and $$y=\lambda x$$ is $$\cfrac { 1 }{ 9 } $$ square units then value of $$\lambda$$ is

The area bounded by the line $$y=x$$, x-axis and ordinates $$x=-1$$ and $$x=2$$ is?

The area bounded by curve $$y=\sin { 2x } \left( x=0\quad to\quad x=\pi  \right) $$ and X-axis is ______

Area of the region bounded by the curve $$y = \cos x$$ between $$x = 0$$ and $$x = \pi$$ is

The area bounded by the curves $$y = -x^2 + 3$$ and $$y = 0$$

The area bounded by $$y = \sin^2 x , x = \dfrac{\pi}{2} $$ and $$x = \pi$$ is