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

The area of the region bounded by the curves $y=x^{3}$,$y=\frac{1}{x}$,and the line $x=2$ in the first quadrant is:

Let the area of the region $\{(x, y): x-2y+4 \geq 0, x+2y^2 \geq 0, x+4y^2 \leq 8, y \geq 0\}$ be $\frac{m}{n}$,where $m$ and $n$ are coprime numbers. Then $m+n$ is equal to

Let $A = \{(x, y) : y^2 \le 4x, y - 2x \ge -4\}$. The area of the region $A$ is

The area enclosed by the parabolas $y = x^2 - 1$ and $y = 1 - x^2$ is (in $/3$)

The area included between the parabolas $y^{2} = 5x$ and $x^{2} = 5y$ is