If $[\cdot]$ denotes the greatest integer function, then $\int_0^{\pi/3}[\tan x]\,dx = $

The area (in square units) bounded by the line $y = x$, the X-axis and the lines $x = -2$ and $x = 4$ is...

The equation of the curve whose slope is $\dfrac{y-1}{x^2+x}$ and which passes through the point $(1, 0)$ is

A body cools from $100^\circ\text{C}$ to $60^\circ\text{C}$ in 20 minutes, the temperature of the surroundings being $20^\circ\text{C}$. The total time taken (in minutes) for the body to cool down to $40^\circ\text{C}$ is ...