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

The area of the region $\{(x, y): x^2+4x+2 \leq y \leq |x+2|\}$ is equal to

The area (in sq. units) bounded by the curve $y=2x-x^2$ and the line $y=-x$ is

If $f(x)$ is a continuous,increasing,and odd function such that $\int_{-1}^{4} f(x) \,dx = 10$ and $\int_{0}^{1} f(x) \,dx = \frac{3}{2}$,then the area bounded by $y = f(x)$,the $x$-axis,and the ordinates $x = -4$ and $x = 4$ is:

The area of the region lying above the $X$-axis and included between the circle $x^{2}+y^{2}=2ax$ and the parabola $y^{2}=ax$, $a>0$ is

The area (in square units) bounded by the curves $x = -2y^2$ and $x = 1 - 3y^2$ is