Question

Based on a preliminary report by a geological survey team, it is estimated that a newly discovered oil field can be expected to produce oil at the rate of
R(t) =
300t^2/(t^3 + 32)+5 (0 ≤ t ≤ 20)
thousand barrels/year, t years after production begins. Find the amount of oil that the field can be expected to yield during the first 3 years of production, assuming that the projection holds true. (Round your answer to the nearest thousand barrels.)

Answer 1

that would be

∫[0,3] 300t^2/(t^3+32) + 5 dt

let
u = t^3 + 32
du = 3t^2 dt
and now you have

∫[32,59] 100/u du + ∫[0,3] 5 dt
= 15 + 100log(59/32)

Answer 2

76