how to derive the formula of average DC voltage of half and full wave rectifier? [closed]

Question

i need the derivations that how these formulae comes

Vavg=Vpeak/pi for half wave rectifier
Vavg=2Vpeak/pi for full wave

Answer 1

Full wave is double of half wave because both 'bumps' are used. That is easy.

Now derive the halfwave:

V(t) = Vpeak*sin(t);

2 PI is a full circle and we only use half of that : 0->PI

Vavg = Vpeak*integral(sin(t),0 -> PI)/2*PI 

indefinite integral of sin(x) = -cos(x)

 = Vpeak*(-cos(PI) + cos(0))/2*PI 
 = Vpeak*(-(-1) +  1) / 2*PI
 = Vpeak ( 1 + 1) / 2*PI
 = Vpeak / PI

that's it.