Pumping stations deliver gasoline

Question

Pumping stations deliver gasoline at the rate modeled by the function D, given by  with t measure in hours and and R(t) measured in gallons per hour. How much oil will the pumping stations deliver during the 3-hour period from t = 0 to t = 3? Give 3 decimal places.



Answer 1

integral (6t)/(1+2t) from 0 to 3.

6t/1+2t = (6t+3-3)/(2t+1) =

(6t+3)/(2t+1) + (-3)/(2t+1) = 3(2t+1)/(2t+1) + (-3)/(2t+1) =

3 + (-3)/(2t+1) now apply the integral and limits, should be straight forward. Turns into

3t - (3/2)ln(2t+1) from 0 to 3

9 - (3/2)ln(7) - ((-3/2)ln(1))

final answer 9-(3/2)ln(7)

Hope this helps.