calculus

posted by Tracy

find the average value of the function
i=15[1-e^(-1/2t)] from t=0 to t=4

A. 7.5(1+e^-2)
B. 7.5(2+e^-2)
C. 7.5(2-e^-2)
D. 7.5(3-e^-2)

  1. Steve

    average value is the integral divided by the interval length. Thinking in terms of area, the integral is the total area, and a rectangle with that same area would have width of the interval, height the average value

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

    Average value = 7.5(1 + 1/e^2) = A

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