The area of the region bounded by the curve $y=x$,the lines $x=1$ and $x=10$ using integration is . . . . . . sq. units.

The area of the region bounded by the $x$-axis and the curves defined by $y = \tan x$ for $(-\pi/3 \le x \le \pi/3)$ 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

The area of the region bounded by the curve $y = \sin(\pi x)$ and the $X$-axis for $x \in [0, 2]$ is . . . . . . sq. units.

The area inside the parabola $y^2 = 4ax$,between the lines $x = a$ and $x = 4a$ is equal to

The smaller area enclosed by the circle $x^{2}+y^{2}=4$ and the line $x+y=2$ is