calculus
posted by Tracy
find the average value of the function
i=15[1e^(1/2t)] from t=0 to t=4
A. 7.5(1+e^2)
B. 7.5(2+e^2)
C. 7.5(2e^2)
D. 7.5(3e^2)

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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