Find the area lying above the $x-$ axis and included between the circle $x^{2}+y^{2}=8x$ and inside the parabola $y^{2}=4x$.

$A$ 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 enclosed between the curve $y = \log_e(x + e)$ and the coordinate axes is

The area of the region bounded by $y = |x - 1|$ and $y = 1$ is

The area of the region bounded by the $y$-axis,$y = \cos x$,and $y = \sin x$ for $0 \leq x \leq \frac{\pi}{2}$ is:

The area of the region bounded by the curve $y = x|x|$,the $x-$axis,and the ordinates $x = 1$ and $x = -1$ is given by: