The area bounded by the curve $y = \log x$,the $x$-axis,and the ordinates $x = 1$ and $x = 2$ is:

$A$ quadratic polynomial $y = f(x)$ with absolute term $3$ neither touches nor intersects the abscissa axis and is symmetric about the line $x = 1$. The coefficient of the leading term of the polynomial is unity. $A$ point $A(x_1, y_1)$ with abscissa $x_1 = 1$ and a point $B(x_2, y_2)$ with ordinate $y_2 = 11$ are given in a Cartesian rectangular system of coordinates $OXY$ in the first quadrant on the curve $y = f(x)$,where $O$ is the origin. The area bounded by the curve $y = f(x)$ and the line $y = 3$ is: (in $/3$)

The odd natural number $a$ such that the area of the region bounded by $y = 1, y = 3, x = 0,$ and $x = y^a$ is $\frac{364}{3}$ is equal to:

Area enclosed by the parabola $ay = 3(a^2 - x^2)$ and $x$-axis is

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

If $(a, 0); a > 0$ is the point where the curve $y = \sin 2x - \sqrt{3} \sin x$ cuts the $x$-axis first,and $A$ is the area bounded by this part of the curve,the origin,and the positive $x$-axis,then: