Question

Oil leaks out of a tanker at a rate of r=f(t) liters per minute, where t is in minutes. If f(t)=Ae^(−kt), write a definite integral expressing the total quantity of oil which leaks out of the tanker in the first hour.

Answer 1

Answer:

The definite integral expressing the total quantity of oil, 'V', which leaks out of the tanker in the first hour is given as follows;

$V = \int\limits^{60}_0 {A \cdot e^{(-k \cdot t)}} \, dt$

Step-by-step explanation:

From the question, we have;

The rate at which oil leaks out of the tanker, r = f(t)

The unit of the oil leak = Liters per minute

The unit of t = Minutes

$If \ f(t) = A \cdot e^{(-k \cdot t )}$

Therefore, we have;

The definite integral expressing the total quantity, 'V', of oil which leaks out of the tanker in the first hour is given as follows;

$V = \int\limits^{60}_0 {A \cdot e^{(-k \cdot t)}} \, dt$

Therefore, we have;

$\int\limits^{60}_0 {A \cdot e^{(-k \cdot t)}} \, dt = \dfrac{A \cdot e ^{60 \cdot k} - A}{k \cdot e ^{60 \cdot k} }$