The area of the region bounded by the curves $y=x^3, y=x^2$ and the lines $x=0$ and $x=2$ is

The substitution required to reduce the differential equation $t^2 d x+\left(x^2-t x+t^2\right) d t=0$ to a differential equation which can be solved by variables separable method is

The equation which represents the system of parabolas whose axis is parallel to $Y$-axis satisfies the differential equation.

Bose-Einstein statistics is applicable to particles with