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

The area bounded by the curve $y=\sin^{2} x$,the $x$-axis,and the lines $x=0$ and $x=\frac{\pi}{2}$ is

The area of the region bounded by the curve $y = \cos x$,$-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$ and the $X$-axis is . . . . . . sq. units.

The line $x=\frac{\pi}{4}$ divides the area of the region bounded by $y=\sin x$, $y=\cos x$ and the $x$-axis $\left(0 \leq x \leq \frac{\pi}{2}\right)$ into two regions of areas $A_1$ and $A_2$. Then $A_1 : A_2$ equals (in $: 1$)

The area bounded by the lines $y=x$,$x=-1$,$x=2$ and the $X$-axis is

Let the straight line $x=b$ divide the area enclosed by $y=(1-x)^2, y=0$,and $x=0$ into two parts $R_1(0 \leq x \leq b)$ and $R_2(b \leq x \leq 1)$ such that $R_1-R_2=\frac{1}{4}$. Then $b$ equals