Application of ...

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

The area bounded by the curved $${ y }^{ 2 }=16x$$  and the line x=4 is  ___________________________.

If $$A_{m}$$ represents the area bounded by the curve $$y=\ln x^{m}$$., the $$x-$$axis and the lines $$x=1$$ and $$x=2$$, then $$A_{m}+m\ A_{m-1}$$ is

The area of the region bounded by the curve $$y=x^{2}-3x$$ with $$y \le 0$$ is

If a curve $$y = a \sqrt { x } +$$ bx passes through the point $$( 1,2 )$$ and the area bounded by the curve, line $$x = 4$$ and $$x$$ axis is $$8$$ square units, then 

The area bounded by the circle $$x^{2}+y^{2}=8$$, the parabola $$x^{2}=2y$$ and the line $$y=x$$ in first quadrant is $$\dfrac{2}{3}+k\pi$$, where $$k=$$

The area enclosed between the curve $$y=\log_{e}\left(x+e\right)$$ and the coordinate axes is

The area of the region formed by $${ x }^{ 2 }+{ y }^{ 2 }-6x-4y+12\le 0,y\le x\quad and\quad x\quad \le \quad \dfrac { 5 }{ 2 } is$$

Area bounded by $$y=2x^{2}$$ and $$y=\dfrac{4}{(1+x^{2})}$$ will be (in sq units)

$$Letf(x)={ sin }^{ -1 }(sin\quad x)+{ cos }^{ -1 }(\quad cos\quad x),\quad g(x)=mx\quad and\quad h(x)=x\quad $$ are three functions. Now g(x) is divided area between f(x),x=$$\pi $$ and y=0 into two equal parts.
The area bounded by the curve y=f(x), x=$$\pi $$ and y=0 is: