The area of the region bounded by the line $y=3x$ and the curve $y=x^2$ in square units is

Area of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ 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 area bounded by the parabola $y^{2}=16x$ and its latus rectum in the first quadrant is

The area of the region bounded by the curve $y = x^2 - x - 6$ and the $X$-axis is . . . . . . sq. units.

The area between the parabola $y = x^2$ and the line $y = x$ is