\[ U_d = \frac{1}{T} \cdot \int_{0}^{T}\hat{U}_S \cdot sin(\omega t) \: dt = \frac{1}{2\pi} \cdot \int_{0}^{2\pi}\hat{U}_S \cdot sin(\omega t) \: d \omega t \]

\[ U_{RMS} = \sqrt{ \frac{1}{T} \cdot \int_{0}^{T} u^2(t) \: dt } = \sqrt{ \frac{1}{2\pi} \cdot \int_{0}^{2\pi} u^2(\omega t) \: d \omega t } \]