# Can't remember how to do this simple definite integral

1. Sep 19, 2010

### astonmartin

If my Force = (-gamma)(dx/dt)
velocity v = dx/dt
Mass m

(m)(dv/dt) = F = (-gamma)(dx/dt)

Now I want to integrate it over kT<= t <= (k+1)T

Rearranging gives me (dv/v) = (-gamma/m)dt

The right side integrates to (-gamma/m)(T), but how do I integrate the left side over kT<= t <= (k+1)T??

Thanks

2. Sep 19, 2010

### HallsofIvy

$$\int \frac{1}{v} dv= ln(v)+ C$$

3. Sep 19, 2010

### astonmartin

^but what does that give me for the definite integral?

ln [v(k+1)T / v(kT)] ?

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