U=\sqrt{\frac{\omega}{2\pi}\int\limits^\frac{2\pi}{\omega}_0U_m^2\sin^2\omega tdt}=
\sqrt{\frac{\omega U_m^2}{2\pi}\left|\frac{t}{\omega}-\frac{\sin2\omega t}{4\omega}\right|^\frac{2\pi}{\omega}_0}=
U_m\sqrt{\frac{\omega}{2\pi}\left(\frac{2\pi}{\omega^2}-\frac{\sin2\omega\frac{2\pi}{\omega}}{4\omega}\right)}=\frac{U_m}{\sqrt\omega}