# The dimensions of an integral

1. Jul 13, 2012

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

$$\int E\ dt$$

Does this have dimensions of energy times time? Or doesn't the dummy variable count?

2. Jul 13, 2012

### Woopydalan

energy times time isn't an insignificant dimension.

3. Jul 13, 2012

I beg to differ, energy times time is action.

edit (isn't an insignificant dimension) I thought you said it was.

4. Jul 13, 2012

5. Jul 13, 2012

### alialice

Yes, this have dimension of energy times time.
An obvious example is
$v=\frac{dx}{dt} \Rightarrow x=\int v dt$
Speed is m/s and space is m.

This is the dimension of an action!

6. Jul 13, 2012