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

The volume of the solid generated by revolving the region bounded by the parabolas $y=x^{2}$ and $x=y^{2}$ about the $y$-axis is:

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

The area of the region bounded by the curve $y = 5 \sin x$,the $X$-axis,and the lines $x = 0$ and $x = \frac{\pi}{2}$ is . . . . . . sq. units.

If the straight line $x=b$ divides 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:

The area bounded by the curve $y = \sin x$ between $x = -\pi/2$ and $x = \pi/2$ is . . . . . . .