Application of ...

The area of the region bounded by the curves $$y = x^2$$ and $$y = |x|$$ is

Area bounded by the curves $$y = \sin x ,$$ tangent drawn to it at $$x = 0$$ and the line $$x = \frac { \pi } { 2 }$$ is equal to

The area enclosed by the line y = x + 1, X- axis and the lines x = -3 and x = 3 is 

The area of the region
A=$$\left [ \left ( x,y \right ) :0\leq y\leq x\left | x \right |+1and -1\leq x\leq 1\right ]$$. in sq. units, is:

As shown in the figure of an ellipse $$\frac{x^{2}}{16}+\frac{y^{2}}{9}=1$$. The area of shaded region is .......
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The area bounded by the parabolas $$y = {\left( {x + 1} \right)^2}\;and\;y = {\left( {x - 1} \right)^2}$$ and the line $$y = \frac{1}{4}$$ is

The area enclosed by parabola $${ y }^{ 2 }=64x$$ and its latus-rectum is $$\lambda $$ then $$3\lambda $$ then $$3\lambda$$ = 

The area enclosed between the curves   $$y = a x ^ { 2 }$$  and  $$x = a y ^ { 2 } ( a > 0 )$$  is  $$1$$ sq. unit, then the value of  $$a$$  is

The area of the region lying between the line $$x-y+2=0 $$ and the curve $$x=\sqrt{y}$$ is

the volume of a solid obtained by revolving about y-axis enclosed between the ellipse $${x}^{2}+9{y}^{2}=9$$ and the straight line $$x+3y=3$$ in the first quadrant is