find the rms value of the function

Question

i=15(1-e^-1/2t) from t=0 to t=4

Answer 1

If we let r = rms of f(t), then

4r^2 = Int(15 - 15e^-1/2t)[0,4]
= 15t + 30e^(-t/2)[0,4]
= [60 + 30/e^2] - [0 + 30]
= 60 + 30/e^2 - 30
= 30 + 30/e^2
=34.06

so, r = 2.92

see wikipedia on root mean square