Question

1 10. Find the average value of the function i = 15(1 - e /2t A. 7.5(1 + e-2) B. 7.5(2 - e-2) C. 7.5(2 + e-2) D. 7.5(3 - e-2) ) from t = 0 to t = 4.

Answer 1

Hello,
Please, see the attached file.
Thanks.

Answer 2

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)


So, the answer is A