Question

Oil leaks out of a tanker at a rate of f(t) gallons per minute, where t is in minutes. enter a definite integral using the variable t, expressing the total quantity of oil which leaks out of the tanker in the first two hours.

Answer 1

The function f(t) gives the amount of oil that leaks out as a function of time (t) where time is measured in minutes.

The total amount of oil that leaks out over some amount of time can be found by integrating f(t) over the interval of time. This of the integral as the sum of each of the amounts when we cut the time up in seconds, or milliseconds...though in reality the intervals are so small they are practically zero...this is why we use an integral rather than a simple sum.

The time is being measured in minutes so 2 hours is 120 minutes. Thus, the total quantity of oil that leaks out is given by $\int\limits^{120}_{0} {f(t)} \, dt$

Be sure to use t (rather that the usual x) because your function is in terms of t.