Application of ...

 Area bounded by $$\displaystyle y=2x-{ x }^{ 2 }$$ & $$\displaystyle (x-1{ ) }^{ 2 }+{ y }^{ 2 }=1$$ in first quadrant, is: 

In what ratio does the x-axis divide the area of the region bounded by the parabolas $$\displaystyle y=4x-x^{2}$$ and $$\displaystyle y=x^{2}-x$$?

For what value of 'a' is the area of the figure bounded by $$\displaystyle y=\frac{1}{x}, y=\frac{1}{2x-1}$$ $$x = 2$$ & $$x = a$$ equal to $$\displaystyle ln\frac{4}{\sqrt{5}}$$?

If the area enclosed by the parabolas $$\displaystyle y=a-x^{2}$$ and $$\displaystyle y=x^{2}$$ is $$\displaystyle 18\sqrt {2}$$ sq. units Find the value of 'a'

Find the area enclosed between the curves $$\displaystyle y=\log_{e}\left ( x+e \right ), x=\log_{e}\left ( 1/y \right )$$ & the x-axis

Let $$f(x)$$ be a continuous function given by $$\displaystyle f\left ( x \right )=2x$$ for $$\displaystyle \left | x \right |\leq 1$$ for $$\displaystyle f\left ( x \right )=x^{2}+ax+b$$ for $$\displaystyle \left | x \right |> 1$$. Find the area of the region in the third quadrant bounded by the curves $$\displaystyle x=-2y^{2}$$ and $$y = f(x)$$ lying on the left of the line $$8x + 1 = 0$$

Let $$\displaystyle C_{1}$$ & $$\displaystyle C_{2}$$ be two curves passing through the origin as shown in the figure A  curve C is said to "bisect the area" the region between $$\displaystyle C_{1}$$ & $$\displaystyle C_{1}$$ if for each point P of C the two shaded regions A & B shown in the figure have equal areas Determine the upper curve $$\displaystyle C_{2}$$ given that the bisecting curve C has the equation $$\displaystyle y=x^{2}$$ & that the lower curve $$\displaystyle C_{1}$$ has the equation $$\displaystyle y=x^{2}/2$$ 

Find the area bounded by $$y = x + sinx$$ and its inverse between $$x = 0$$ and $$x = \displaystyle 2\pi$$

The smaller area enclosed by $$y=f(x)$$, where $$f(x)$$ is polynomial of least degree satisfying $$\displaystyle{ \left[ \lim _{ x\rightarrow 0 }{ 1+\frac { f\left( x \right)  }{ { x }^{ 3 } }  }  \right]  }^{ \tfrac { 1 }{ x }  }=e$$ and the circle $$x^2+y^2=2$$ above the $$x-$$axis is

The area of the region described by $$\left \{(x, y)/ x^{2} + y^{2} \leq 1\ and\ y^{2} \leq 1 - x\right \}$$ is