mathematics

find the mean and RMS of v=25sin50πt
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.

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  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

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