Notation for some integrals

Question

I've seen some problems where the OP writes integrals in this form

$$\int {dt} f\left( t \right)$$

or for double integrals

$$\int {dx} \int {dtf\left( {t,x} \right)} $$

Do they represent another kind of integrals, or is it just notation?

Answer 1

This is just notation. In general, $$\int f(t) dt = \int dt f(t)$$

In fact you can move the $dt$ term anywhere you want--as long as it remains within its corresponding integral. So $$\int dx \int dt f(t, x) = \int \left( \int f(t, x) dt \right) dx = \int \int f(t, x) dt dx$$ but $$\int dx dt \int f(t, x) \neq \int \int f(t, x) dt dx$$ (And the left-hand side is nonsense, since it's right integral has no $d$ term.)