Calculus II
posted by Patricia .
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.

Calculus II 
Steve
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
Respond to this Question
Similar Questions

calculus
oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume increases at a constant rate of 2000 cubic centimeters per minute. The oil slick takes the form of a right circular cylinder with both its … 
calc
oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume increases at a constant rate of 2000 cubic centimeters per minute. The oil slick takes the form of a right circular cylinder with both its … 
Calculus rates
A tanker is spilling oil into the water resulting in an oil slick that is close to circular. At te time that the slick's diameter is growing at a rate of 8 ft/sec, the diameter is 250 feet. At what rate is the area of the oil sick … 
Math
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 … 
calculus
I have spilled 200cm^3 of vegetable oil on my kitchen floor. The resulting oil slick can be modeled as a cylinder with a very small height; the height is decreasing at a rate of 1/1000πcm/sec and the radius is currently 50cm. … 
Math
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 … 
Math
A new oil field has just begun production. The first oil removed is the easiest to get out, and so production falls as time goes on. The instantaneous rate at which oil can be extracted is 14% of the amount of oil remaining per year. … 
Math
A new oil field has just begun production. The first oil removed is the easiest to get out, and so production falls as time goes on. The instantaneous rate at which oil can be extracted is 14% of the amount of oil remaining per year. … 
Math
A new oil field has just begun production. The first oil removed is the easiest to get out, and so production falls as time goes on. The instantaneous rate at which oil can be extracted is 14% of the amount of oil remaining per year. … 
Math
A new oil field has just begun production. The first oil removed is the easiest to get out, and so production falls as time goes on. The instantaneous rate at which oil can be extracted is 6% of the amount of oil remaining per year. …