# Finding the total production of oil given a rate.

1. Jan 29, 2012

### turbokaz

1. The problem statement, all variables and given/known data
Oil is ﬂowing from a well in a continuous stream at a rate of
f(t) =54/(t + 3)^2 barrels per month (in multiples of 100). Find
the total oil produced by the well in its second
three months of operation.

2. Relevant equations

3. The attempt at a solution
Answer choices are 300, 250, 350, 450, 400.
Now, I found the problem worded strangely, but here goes. f(t) is a derivative, so I took the integral of f(t) and got -54/(t+3). The question asks for how much is produced in its second three months, so I took that as 6 months total. Plug in 6 for t and get -6 barrels. But it is in multiples of 100, so 600 barrels produced in the 6 months? So if its asking for oil produced in its "second three months of operation", then in those three months it produced 300 barrels? I hate the wording of the question, and that is the only way I could interpret it and get an answer choice that was provided. Your thoughts?

2. Jan 29, 2012

### tjackson3

I take "second three months" to mean between t=4 and t=6 (where the first three are t=1 to t=3, though it's ambiguous enough that it could be between t=0 and t=2). So you evaluate the definite integral

$$\int_4^6\ f(t)\ dt$$

3. Jan 29, 2012

### Dick

I would integrate 5400/(t+3)^2 for t=3 to t=6. So I'd probably say 300 as well. But not quite for the reasons you give.