Application of ...

The area bounded by the curves $$y=\sin x,y=\cos x$$ and $$y-$$axes in first quadrant is:

Consider the function $$f\left( x \right) = \left| {x - 1} \right| + {x^2},\,\,where\,\,x \in R$$
What is the area of the region bounded by X-axis, the  curve $$y = f\left( x \right)$$ and the two ordinates $$x = \frac{1}{2}\,\,\,and\,\,\,x = 1$$.

The area bounded by $$y = cos \, x , \, y = x + 1 , \, y = 0$$ is 

The area enclosed between the curve $$y^2 = x \, and \, y = |x|$$ is

The area bounded by the curve f(x) = x + sin x and its inverse function between the ordinates $$x = 0 \, and \,  x = 2 \pi$$ is

Ratio in which curve $$\left| y \right| + x = 0$$ divides the area bounded by curve $$y = {\left( {x + 2} \right)^2}$$ and coordinate axes, is-

Consider the functions $$f(x)$$ and $$g(x)$$, both defined from $$R \rightarrow R$$ and are defined as $$f(x)=2x-x^{2}$$ and $$g(x)=x^{n}$$ where $$n \in N$$. If the area between $$f(x)$$ and $$g(x)$$ in first quadrant is $$1/2$$ then $$n$$ is not a divisor of :

The area bounded by $$y=x^2, y=[x+1], x \leq 1 $$ and the y-axis is, where $$[.]$$ is greatest integer function

The area between the curves y = tanx, y = cotx and x - axis in the interval $$[0,\pi / 2]$$ is 

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