(i) RMS Output Voltage : The average value of the output voltage is given by

$$E_{0(\mathrm{av})}=\frac{1}{2 \pi} \int_{0}^{2 \pi} e_{0}(\omega t) \mathrm{d} \omega t$$

Now, rms value of the output voltage is given by

$$E_{0(\mathrm{rms})}=\sqrt{\frac{1}{2 \pi} \int_{0}^{\pi / 2} e_{0}^{2}(\omega t) \mathrm{d} \omega t}=\sqrt{\frac{4}{2 \pi} \int_{0}^{\pi / 2} e_{0}^{2}(\omega t) …