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Can't remember how to do this simple definite integral

  1. Sep 19, 2010 #1
    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??

  2. jcsd
  3. Sep 19, 2010 #2


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    Science Advisor

    [tex]\int \frac{1}{v} dv= ln(v)+ C[/tex]
  4. Sep 19, 2010 #3
    ^but what does that give me for the definite integral?

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