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Basic calculus question (kinematics)

  1. Dec 4, 2012 #1
    Could someone point me to the proof or reasoning behind the steps:

    1) a = dv/dt
    2) a dt = dv
    3) ∫a dt = ∫dv

    I know this works, but I'm missing understanding in the math behind it, and I'm not sure what to type into google.

    Thank you very much
  2. jcsd
  3. Dec 4, 2012 #2


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    1) is the definition of acceleration, i.e, the derivative of velocity with respect to time.
    2)+3) are silly pseudo-steps, the mathematically CORRECT next step from 1) is:
    2a) [tex]\int{a}dt=\int\frac{dv}{dt}dt[/tex]
    3a) Now, using integration by substitution on the right-hand integral, we may, if we like, rewrite 2a) as:
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