The area bounded by the parabola $x^{2}=4y$ and the lines $y=2$,$y=4$ and the $Y$-axis is

The area bounded by the curve $y = \sin \left(\frac{x}{3}\right)$,the $x$-axis,and the lines $x = 0$ and $x = 3\pi$ is

$A$ farmer $F_1$ has a land in the shape of a triangle with vertices at $P(0,0)$,$Q(1,1)$,and $R(2,0)$. From this land,a neighbouring farmer $F_2$ takes away the region which lies between the side $PQ$ and a curve of the form $y = x^n$ $(n > 1)$. If the area of the region taken away by the farmer $F_2$ is exactly $30\%$ of the area of $\triangle PQR$,then the value of $n$ is:

Let $f(x) = \min \{\sin^{-1} x, \cos^{-1} x\}$. Then the area bounded by $f(x)$ and the $x$-axis is:

The area of the region (in sq. units) enclosed by the curve $y=x^3-19x+30$ and the $x$-axis is

Area enclosed by the curve $y = f(x)$ that is defined parametrically as $x = \frac{1 - t^2}{1 + t^2}, y = \frac{2t}{1 + t^2}$ (where $t \in R$) is equal to