This is an extremely basic question but I am curious, can the same function be equivalent when it has different parameters.
For instance if let's say I had an equation p(r) = $ \frac {r}{a} $
I then had an equation
E = $ \frac{\int n(r')r}{n(r)} $
In this instance we assume n(r) is proportional to p(r).
n(r) $ \propto $ p(r)
Does this equation then become
E = $ \frac{\int p(r')r}{p(r)} $
and then the p(r) and p(r') terms cancel out of $ \frac{\int p(r') r}{p(r)} $
leaving just $ \int r$
If so, what is the proof for this.
