Application of ...

The area of the region bounded by the curve $$y=2x-x^2$$ and the line $$y=x$$ is ________ square units.

The area bounded by the curve $$ y =x^2 +2x +1 $$ and tangent at $$ ( 1 , 4) $$ and y -axis and 

If $$ A_n $$ is the area bounded by $$ y = ( 1 -x^2)^n $$ and coordinates axes , $$ n \epsilon N $$, then 

The area enclosed between the curves $$y=log_{e}(x+e)\, , \,x=log_{e}\left ( \dfrac{1}{y} \right ) $$ and the $$x-axis$$ is

If $$\displaystyle \left ( \alpha ^2,\alpha  - 2 \right )$$ be a point interior to the region of the parabola $$\displaystyle y^2 = 2x$$ bounded by the chord joining the points $$\displaystyle \left ( 2,2 \right ) and \left ( 8,-4 \right )$$ then $$\alpha$$ belongs to the interval

The area of the region enclosed by the curves $$y=x\log x$$ and $$y=2x-2x^2$$ is

Area of the region bounded by the curve $$ y =e^x, y=e^{-x} $$ and the straight line x= 1 given by

The area bounded by the curve $$ y = (x) $$ the x-axis and the ordinate $$x= 1$$ and $$x = b$$ is $$(b- 1)$$ $$cos ( 3b + 4)$$, then $$f(x)$$ is given by 

The area of the closed figure bounded by $$y=\dfrac{x^{2}}{2}-2x+2$$ and the tangents to it at $$(1,\dfrac{1}{2}) $$ and $$(4,2)$$ is  

The area of the region in 1st quadrant bounded by the $$y-axis, \, y=\dfrac{x}{4}, \, y=1+\sqrt{x} \, and\, y= \dfrac{2}{\sqrt{x}} $$