Question

current attempt in progress
oil leaks out of a tanker at a rate of ( r = f(t) ) gallons per minute, where ( t ) is in minutes. write a definite integral expressing the total quantity of oil (in gallons) which leaks out of the tanker in the first four hours.
the total quantity of oil which leaks out of the tanker in the first four hours is
( \bigcirc int_{0}^{240} f(t) d t )
( \bigcirc int_{0}^{4} f(t) d t )
( \bigcirc int_{0}^{4} \frac{1}{f(t)} d t )
( \bigcirc int_{0}^{240} \frac{1}{f(t)} d t )

Explanation:

Step1: Convert hours to minutes

Since \(1\) hour \( = 60\) minutes, then \(4\) hours \(=4\times60 = 240\) minutes.

Step2: Use the formula for total quantity from rate - function

The total quantity \(Q\) of a substance flowing (or leaking in this case) at a rate \(r = f(t)\) (where \(t\) is the time variable) over an interval \([a,b]\) is given by \(Q=\int_{a}^{b}f(t)dt\). Here, \(a = 0\) (starting time) and \(b = 240\) (ending time in minutes).

Answer:

\(\int_{0}^{240}f(t)dt\)