Application of ...

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

The area enclosed by the curve $$\left[x+3y\right]=\left[x-2\right]$$ where $$x\epsilon\left[3,4\right)$$ is (where $$[.]$$ denotes greatest integer function.)

Area bounded by the parabola $${ x }^{ 2 }=36y$$ and its latus rectum is 

The area of the closed figure bounded by $$y = x , y = - x \&$$ the tangent to the curve $$y = \sqrt { x ^ { 2 } - 5 }$$ at the point $$( 3,2 )$$ is:

Area of region bounded by $$[x]^2=[y]^2$$ if $$x\in [1,5]$$ where [.] represents the greatest integer function is-

If $$\left[ \begin{array} { c c c } { 4 a ^ { 2 } } & { 4 a } & { 1 } \\ { 4 b ^ { 2 } } & { 4 b } & { 1 } \\ { 4 c ^ { 2 } } & { 4 c } & { 1 } \end{array} \right] \left[ \begin{array} { c } { f ( - 1 ) } \\ { f ( 1 ) } \\ { f ( 2 ) } \end{array} \right] = \left[ \begin{array} { c } { 3 a ^ { 2 } + 3 a } \\ { 3 b ^ { 2 } + 3 b } \\ { 3 c ^ { 2 } + 3 c } \end{array} \right]$$  $$f ( x )$$  is a quadratic function and its maximum value occurs at a point  $$V. A$$  is a point of intersection of  $$y = f ( x )$$  with  $$x$$ -axis and point  $$B$$  is such that chord  $$AB$$  subtends a right angled at  $$V .$$  Find The area enclosed by  $$f ( x )$$  and chord  $$A B .$$

If the area between the curves y=kx2 and x=ky2 is 1 
then k is 

The area between the parabola $${ y }^{ 2 }=4x$$, normal at one end of latusreetum and X-axis sin sq. units is

Area bounded by Curve $${ y }^{ 2 }=4x,y$$ axis and line y=3 is : 

If $${ A }_{ n }$$ is the area bounded by y=x and y=$${ x }^{ n },n\epsilon N$$, then $${ A }_{ 2. }.{ A }_{ 3 }...{ A }_{ n }=$$