The area bounded by the curves $y^2 = 4x$ and $x^2 = 4y$ is

The area (in square units) of the region enclosed by the two circles $x^2+y^2=1$ and $(x-1)^2+y^2=1$ is

Let $f: R \to R$ be a function such that $f(x) + 3f(\frac{\pi}{2} - x) = \sin x, x \in R$. Let the maximum value of $f$ on $R$ be $\alpha$. If the area of the region bounded by the curves $g(x) = x^2$ and $h(x) = \beta x^3, \beta > 0$,is $\alpha^2$,then $30\beta^3$ is equal to ————

The area (in square units) of the region bounded by the parabola $y^2=4(x-2)$ and the line $y=2x-8$ is:

The area of the region,bounded by the curves $y=\sin ^{-1} x+x(1-x)$ and $y=\sin ^{-1} x-x(1-x)$ in the first quadrant,is

Let for $x \in R$; $f(x) = \frac{x+|x|}{2}$ and $g(x) = \begin{cases} x, & x < 0 \\ x^2, & x \geq 0 \end{cases}$. Then the area bounded by the curve $y = (f \circ g)(x)$ and the lines $y = 0$,$2y - x = 15$ is equal to $...........$.