find the average value of the function

Question

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)

Answer 1

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