The area of the region bounded by the parabola $$y=x^2+1$$ and lines $$y=x+1, y=0, x=\frac{1}{2}$$ and $$x=2$$ is

Let the functions $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ be defined by $$f(x)=e^{x-1}-e^{-|x-1|}$$ and $$g(x)=\frac{1}{2}\left(e^{x-1}+e^{1-x}\right)$$. Then, the area of the region in the first quadrant bounded by the curves $$y=f(x), y=g(x)$ and $x=0$$ is.

What is the area enclosed by the parabola described by $${(y - 2)^2} = (x - 1)$$, its tangent line at the point (2, 3), and the X-axis?

The area enclosed by the curves $$y = \sin x + \cos x$$ and $$y = |\cos x - \sin x|$$ over the interval $$\left[ {0,{\pi \over 2}} \right]$$ is

The area of one curvilinear triangle formed by curves y = sin x, y = cos x and X-axis, is

Circle centered at origin and having radius $$\pi$$ units is divided by the curve y = sin x in two parts. Then area of upper parts equals to