I have been reading some articles and I see that there is an analogue of the dot product for functions in the form of an integral. However, I am confused by the fact that there seems to be 2 forms:
- $\int f_1(x)f_2(x)dx$
- $\int w(x)f_1(x)f_2(x)dx$ where $w(x)$ is called the weight function
What is going on? Perhaps the 1st case is a special case of the second where the weight function equals 1? When do you need the weight function?