The area bounded by $y=x+1$, $y=\cos x$ and the $X$-axis is

The value of $\int \limits_0^{2 \pi} \min \{|x-\pi|, \cos ^{-1}(\cos x)\} d x$ is

The area in the first quadrant between the ellipses $x^{2} + 2y^{2} = a^{2}$ and $2x^{2} + y^{2} = a^{2}$ is:

If the area of the region bounded by the curves $y = x^2$,$y = \frac{1}{x}$ and the lines $y = 0$ and $x = t$ $(t > 1)$ is $1 \, \text{sq. unit}$,then $t$ is equal to

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 sq units) bounded by the curves $y^2=4x$ and $x^2=4y$ is