The area of the region enclosed by the parabola $y=4x-x^2$ and $3y=(x-4)^2$ is equal to

The area (in square units) of the region bounded by the curves $x=y^2$ and $x=3-2y^2$ is

The area (in square units) bounded by the curves $y^2=4x$ and $x^2=4y$ in the plane 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

The area of the region in the first quadrant inside the circle $x^2+y^2=8$ and outside the parabola $y^2=2x$ is equal to:

The area bounded by the curve $y = e^x$ and the lines $y = |x - 1|, x = 0, x = 2$ is given by