What are the dimensions of an integral in terms of energy and time?

[help1please]

Homework Statement

Homework Equations

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?

 

[member 392791]

energy times time isn't an insignificant dimension.

 

[help1please]

energy times time isn't an insignificant dimension.

I beg to differ, energy times time is action.

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

 

[help1please]

Now can someone answer my question please?

 

[alialice]

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?

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.

energy times time isn't an insignificant dimension.

This is the dimension of an action!

 

[AbigailM]

Yes your integral (the action) does have units of Energy x Time. Remember though, in physics you may come across different types of actions, that have different units. For fields, there is an action that is integrated over spatial dimensions rather than time.

http://en.wikipedia.org/wiki/Action_(physics)#Mathematical_definition