So, I just have a small question.
Given that $\langle f,g\rangle=\langle g,f\rangle$, $\forall f, g\in V$. One of the Inner Product Space axioms.
So, I prove by saying $\langle f,g\rangle = \int f(x)g(x)dx$ and $\langle g,f\rangle = \int g(x)f(x)dx$. So these are obviously equivalent, but how do I justify that the order of $g(x)$ and $f(x)$ in the integral doesn't matter?
Thanks in advance :)