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Homework Help: The dimensions of an integral

  1. Jul 13, 2012 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution

    Just a question on dimensional analysis here.

    I believe that when an integral is taken with respect to time for instance, dt appears as a dummy variable yes? Imagine we had

    [tex]\int E\ dt[/tex]

    Does this have dimensions of energy times time? Or doesn't the dummy variable count?
  2. jcsd
  3. Jul 13, 2012 #2
    energy times time isn't an insignificant dimension.
  4. Jul 13, 2012 #3
    I beg to differ, energy times time is action.

    edit (isn't an insignificant dimension) I thought you said it was.
  5. Jul 13, 2012 #4
    Now can someone answer my question please?
  6. Jul 13, 2012 #5
    Yes, this have dimension of energy times time.
    An obvious example is
    [itex] v=\frac{dx}{dt} \Rightarrow x=\int v dt [/itex]
    Speed is m/s and space is m.

    This is the dimension of an action!
  7. Jul 13, 2012 #6
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