How to model a generic low frequency signal?
Note that you can also use Parseval's theorem. Assuming that $f(t)$ and $g(t)$ are both real-valued we have:

$$\int_{-\infty}^{\infty}f(t)g(t)dt=\frac{1}{2\pi}\int_{-\infty}^{\infty}F(\omega)G^*(\omega)d\omega\tag{1}$$

If $g(t)$ is a narrow-band low-pass signal, i.e., if we can model $G(\omega)$ as $G(\omega)\approx G(0)\text{rect}(\omega/\Delta\omega)$, and if we can assume that $F(\omega)$ is approximately constant (equal to $F(0)$) in the narrow interval $\Delta\omega$, then we can write

$$\frac{1}{2\pi}\int_{-\infty}^{\infty}F(\omega)G^*(\omega)d\omega\approx\frac{1}{2\pi}F(0)G^*(0)\Delta\omega\tag{2}$$

where $\Delta\omega$ is twice the bandwidth of $g(t)$ (because the bandwidth is defined as the support at positive frequencies). With

$$F(0)=\int_{-\infty}^{\infty}f(t)dt$$

and

$$G^*(0)=G(0)=\int_{-\infty}^{\infty}g(t)dt$$

we obtain from $(1)$ and $(2)$

$$\int_{-\infty}^{\infty}f(t)g(t)dt\approx\frac{\Delta\omega}{2\pi}\int_{-\infty}^{\infty}f(t)dt\int_{-\infty}^{\infty}g(t)dt\tag{3}$$