Application of ...

The area of the region bounded by $$x^2+y^2-2x-3=0$$ and $$y=|x|+1$$ is

The value of the parameter $$a$$ such that the area bounded by $$y=a^{2}x^{2}+ax+1,$$ coordinate axes and the line $$x=1$$ attains its least value, is equal to 

The area bounded by $$ y=\sec^{-1}x\, y=cosec^{-1}x \,$$ and line $$x-1=0$$ is

The area of the closed figure bounded by $$ x=-1, \, x=2$$ and $$ y= -x^2+2, \, x\leq 1$$ and $$y= 2x-1 ,\, x>1$$ and the abscissa axis is 

The area of the region whose boundaries are defined by the curves $$y=2 \ cos\,x, \, y=3 \ tan\,x$$ and the $$y-axis$$ is 

A tangent having slope of $$-\dfrac{4}{3} $$ to the ellipse $$\dfrac{x^{2}}{18}+ \dfrac{y^{2}}{32}=1 $$ intersects the major and minor axes at points A and B respectively. If C is the center of the ellipse , then area of the triangle ABC is

The area enclosed by the curves $$xy^2 =a^2(a-x)$$ and $$(a - x) y^2 = a^2x$$ is

The sequence $$S_0,S_1,S_2$$.... forms a G.P with common ratio

The area of the loop of the curve, $$ay^2 =x^2 (a - x)$$ is 

The area enclosed by the circle $$x^{2} + y^{2} = 2$$ is equal to