The area of the region given by $\{(x, y): xy \leq 8, 1 \leq y \leq x^2\}$ is :

The area (in sq. units) of the region $\{(x, y) \in R^{2}: x^{2} \leq y \leq 3-2x\}$ 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

In the interval $(0, \pi / 2)$,the area lying between the curves $y = \tan x$ and $y = \cot x$ and the $X$-axis is:

The area (in square units) of the region enclosed between the parabola $y^2=2x$ and the line $y=4x-1$ is:

The area (in sq. units) bounded by the curve $x^2+2x+y-3=0$,the $X$-axis and the tangent at the point where the curve meets the $Y$-axis is