TITLE: Integral dx term sanity check
QUESTION [5 upvotes]: In my lecture slides, the dx term occasionally precedes the function being integrated. I understand that dx means "an infinitely small width of x" but does the definition of integration require it to be the final term?
My question really is: 
Does the following equality hold?
$\int (f(x)~dx) = \int (dxf(x))  $

REPLY [3 votes]: You can read (as a heuristic) $\displaystyle \int f(x)\,dx$ as the sum of the products of $f(x)$ by the width $dx$. These are 'real numbers' so commute, so yes they mean the same thing.