Pumping stations deliver gasoline at the rate modeled by the function D, given by D(t)= 6t/(1+2t) 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.

Question

Pumping stations deliver gasoline at the rate modeled by the function D, given by D(t)= 6t/(1+2t)  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.

I'm pretty sure you don't plug in 3 to the equation so I am wondering what you do do.

Steve · Accepted Answer

gallons = rate * time, so you get ∫[0,3] D(t) dt = ∫[0,3] 6t/(1+2t) dt = 9 - (3log7)/2 = 6.0811