Find the amount of oil that the field can be expected to yield during the first 6 years of production, assuming that the projection holds true

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)=((600t^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 6 years of production, assuming that the projection holds true. (Round your answer to the nearest thousand barrels.)

Answer 1

Answer 2

The production function integrates very easily with a u-substitution.

Simply integrate both terms and evaluate the definite integral between 0 and 6.