find the mean and RMS of v=25sin50πt

Question

over the range t=0 to t=20ms using integration.

i have integrated to: v=-cos(50πt)/2π+c

but i don't know how to get the mean and rms.

Answer 1

rms = root of the mean of the square.

v = 25 sin 50πt
we want the square:
v^2 = 625 sin^2(50πt)
the mean is ∫[0,20] v^2 dv / 20
= 1/20 ∫[0,20] 625 sin^2(50πt) dt
= 312.5
so, the root mean square is
17.68

the mean is just
1/20 ∫[0,20] 25 sin(50πt) dt = 0