Inner Product of Functions

The inner product of two functions $f_1$ and $f_2$ defined on the interval $[a,b]$, the inner product is defined as:

$$⟨f_1,f_2⟩={\int }_a^b{f}_1(x)f_2(x)dx$$

This operation results in a scalar value.

Note that the inner product is also a function of the interval, and that changing the interval changes the inner product.