# Inner product of functions

## Main Question or Discussion Point

What is the proof that the inner product of two functions f(x) and g(x) is

$$\int_{a}^{b} f(x)g(x)dx$$

Or is this actually a definition of the inner product for functions? If it is a definition, then what is it based on?

Thank you

Last edited:

arildno
$$<f,g>\mid_{w}=\int_{a}^{b}f(x)g(x)w(x)dx$$