Oil is flowing from a well in a continuous stream at a rate of f(t)= (108) / (t+3)^2?

Question

barrels per month (in mutiples of 100). Find the total oil produced by the well in its second three months of operation.

Answer 1

f ( t ) = 108 / (t + 3) ²
In second month t = 2
f ( 2 ) = 108 / 25
No. of barrels = (108 / 25) x 100 = 432 barrels

Answer 2

That would be the integral of 108/(t+3)^2, assuming t is in months.

This is -108/(x + 3)

I assume "second three months" means months 4 through 6 (1 through 3 are the "first three months").

This would be 24/7 * 100 barrels or 342.857 barrels

Answer 3

Integrate f(t) = 108/(t+3)^2 from t = 4 to 6 or

108 int(dt/(t+3)^2)

let u = t +3, du = dt so we want
108 int (u^(-2) du)
= - 108 u^(-1)
= - 108 (t+3)^(-1), t from 4 to 6, or

= -108 [ 1/(6+3) - 1/(4+3)
= -108 [ 1/9 - 1/7]
= 15.42 hundred barrels, by my calculations.

Answer 4

So you need f(4)+f(5)+f(6) = 108/49 + 108/64 + 108/81 = 5.225 = 522.5 barrels