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

Let $\Delta$ be the area of the region $\left\{( x , y ) \in \mathbb{R} ^2: x ^2+ y ^2 \leq 21, y ^2 \leq 4 x , x \geq 1\right\}$. Then $\frac{1}{2}\left(\Delta-21 \sin ^{-1} \frac{2}{\sqrt{7}}\right)$ is equal to

The area bounded by the curves $y=\frac{1}{4}\left|4-x^2\right|$ and $y=7-|x|$ is

If the area enclosed between the curves $y = kx^2$ and $x = ky^2$ $(k > 0)$ is $1$ square unit,then $k$ 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 square units) bounded by the curves $y=x^3$, $y=x$ and $-1 \leq x \leq 1$ is: