# What is the meaning of the integral of position? [duplicate]

Jerk, $j(t)=\dddot x(t)$, acceleration, $a(t)=\ddot x(t)$ and velocity, $v(t)=\dot x(t)$ are derivatives of position, $x(t)$. What is the meaning of the integral of position?

For example, one could write

$$\int x \mathrm{d}t = \int x \frac{\mathrm{d}t}{\mathrm{d}x}\mathrm{d}x = \int x\frac{1}{v} \mathrm{d}x$$

which reminds the equation for expected value.

## marked as duplicate by sammy gerbil, stafusa, user259412, M. Enns, Kyle KanosApr 23 '18 at 10:21

• if you perform the integral over a bounded domain (say $0\leq t\leq T$) than this gives the mean-position ($T$-times it). There is no further meaning to my knowledge – Bort Dec 14 '15 at 14:45