Application of ...

The area bounded by the curves $$y=xe^{x},y=xe^{-x}$$ and the line $$x=1$$, is

The ratio of the areas of two regions of the curve $$C_1 : 4x^2 + \pi^2y^2 = 4\pi^2$$ divided by the curve $$C_2 : y = -sgn \left(x - \dfrac{\pi}{2}\right) \cos x$$ (where sgn(x) denotes signum function) is - 

If $$z$$ is not purely real then area bounded by curves $$lm\left(z+\dfrac{1}{z}\right) = 0$$ and $$|z-1| = 2$$ is (in square units)-

Area bounded by the curves y= $$[\frac{x^{2}}{64}+2],y=x-1$$ and x=0 above x-axis is where $$[.]$$ denotes greatest $$x$$.

The graphs of $$f(x)=x^{2}$$ and $$g(x)=cx^{3}(c>0)$$ intersect at the points $$(0, 0)$$ and $$(\dfrac{1}{c}, \dfrac{1}{c^{2}})$$. If the region which lies between these graphs and over the interval $$[0, \dfrac{1}{c}]$$ has the area equal to $$(\dfrac{2}{3})sq.\ units$$, then the value of $$c$$ is :

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

The area bounded by circles $$x^2+y^2=r^2$$, $$r=1, 2$$ and rays given by $$2x^2-3xy-2y^2=0$$($$y > 0$$) is?

In a system of three curves $$C_{1}, C_{2}$$ and $$C_{3}, C_{1}$$ is a circle whose equation is $$x^{2}+y^{2}=4$$. $$C_{2}$$ is the locus of orthogonal tangents drawn on $$C_{1}. C_{3}$$ is the intersection of perpendicular tangents drawn on $$C_{2}$$. Area enclosed between the curve $$C_{2}$$ and $$C_{3}$$ is-

The area bounded by the curve $$y = f(x)$$ the x-axis & the ordinates x=1 & x=b is  $$\left( {b - 1} \right)\,\sin \left( {3b + 4} \right).\,then\,f\left( x \right)is:$$