Question

For some constants A and B, the rate of production, R(t), of oil in a new oil well is modelled R(t)=A+Be^(-t)sin(2πt) where t is the time in years, A is the equilibrium rate, and B is the "variability" coefficient. Find the total amount of oil produces in the first N years of operation. Then find the average amount of oil produced per year over the first N years.

Answer 1

total amount is ∫[0,N] R(t) dt
use integration by parts twice for this:

-e^(-t)/(1+4π^2) (sin 2πt + 2πcos 2πt)

average amount is Total/N