#### To determine

**To represent:**

What does ∫0120rtdt represent.

#### Answer

The change in the volume from 0 minute to 120 minutes. Or in other words it is the total volume of oil leaked in 2 hours.

#### Explanation

**1) Concept:**

The Net Change Theorem: The integral of a rate of change is the net change.

∫abF'xdx=Fb-Fa

**2) Given:**

∫0120r(t)dt

3) **Calculation:**

Consider the integral,

∫510rtdt, where rt is the rate oil leaks from a tank.

Let V (t) be the volume of a tank then,V't=r(t)

Now, substitute the value V'(t)=rt in ∫0120r(t)dt.∫0120rtdt=∫0120V'tdt

By using the Net Change Theorem,

∫0120V'(t)=V120-V(0)

Hence,

∫0120r(t)=V120-V(0)

The integral ∫0120r(t)dt represents the change in volume from 0 minute to 120 minutes. That is the total volume of oil leaked in first 2 hours.

**Conclusion:**

Therefore, the integral ∫0120r(t)dt represents the change in volume from 0 minute to 120 minutes . That is the total volume of oil leaked in first 2 hours.