An oil company is planning to extract oil from one of its fields, starting today at t=0, where t is time measured in years. It has a choice between two extraction profiles f and g giving the instantaneous flow of oil per year. Both extraction profiles last for 10 years, with f(t) = 10t2 - t3 and g(t) = t3 - 20t2 + 100t for t in [0,10]. The company sells oil at a price per unit by p(t) = 1 + 1 / (t+1). Total revenue is given by ∫010 p(t)f(t) dt and ∫010 p(t)g(t)dt respectively. Compute these integrals. Which of the extraction profiles should be chosen?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.