Application of ...

The parabolas $$y^{2}=4x$$ and $$x^{2}=4y$$ divide the square region bounded by the lines $$x=4, y=4$$ and the coordinate axes. If $$S_{1}$$, $$S_{2}$$, $$S_{3}$$ are respectively the areas of these parts numbered from top to bottom; $$S_{1}: S_{2}: S_{3}$$ is

The area bounded by parabolas $$y=x^{2}+2x+1$$ & $$y=x^{2}-2x+1$$ and the line $$\displaystyle y=\frac{1}{4}$$ is equal to

$$\int_{0}^{\pi /2}min\left \{ \sin x, \cos x \right \}dx$$ equals

The  area bounded by $${ y }^{ 2 }+8x=16$$ and $${ y }^{ 2 }-24x=48$$ is $$\displaystyle \frac { a\sqrt { 6 }  }{ c } $$, then $$a+c=$$

The area enclosed between the curves $$y=x^3$$ and $$y=\sqrt{x}$$ is (in square units)

Find the area bounded by $$\displaystyle y = \cos ^{-1}x,y=\sin ^{-1}x$$ and $$y-$$axis

Consider two curves $$\displaystyle C_{1}:y=\frac{1}{x}$$ and $$\displaystyle C_{2}$$ : $$y = \displaystyle lnx$$ on the xy plane Let $$\displaystyle D_{1}$$ denotes the region surrounded by $$\displaystyle C_{1}$$, $$\displaystyle C_{2}$$ and the line $$x = 1$$ and $$\displaystyle D_{2}$$ denotes the region surrounded by $$\displaystyle C_{1}$$, $$\displaystyle C_{2}$$ and the line $$x = a$$ If $$\displaystyle D_{1}$$=$$\displaystyle D_{2}$$ then the value of 'a':

Suppose $$y = f(x)$$ and $$y = g(x)$$ are two functions whose graphs intersect at three points $$(0, 4), (2, 2)$$ and $$(4, 0)$$ with $$f(x) > g(x)$$ for $$0 < x < 2$$ and $$f(x) < g(x)$$ for $$2 < x < 4 $$. if $$\displaystyle \int_{0}^{4}\left ( f(x)-g(x) \right )dx=10$$ and $$\displaystyle \int_{2}^{4}\left ( g(x)-f(x) \right )dx=5$$, the area between two curves for $$0 < x < 2$$, is:

Area of the region enclosed between the curves $$\displaystyle x=y^{2}-1$$ and $$\displaystyle x = \left | y \right |\sqrt{1-y^{2}}$$ is

Find the area of the region bounded by the curves $$\displaystyle x=\frac{1}{2},x=2,y=logx$$ and $$y=2^{x}$$