#### To determine

**To represent:**

What does ∫abI(t)dt represent.

#### Answer

The integral ∫abItdt represents the total change in the charge from time t= b to t = a. Or in other words it is the total amount of charge passed through between t = a and t = b.

#### Explanation

**1) Concept**:

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

∫abF'xdx=Fb-Fa

**2) Given:**

∫abItdt& It=Q'(t)

**3) Calculation:**

Consider the given integral,

∫abItdt, where It=Q't

Now substitute the value It=Q't in ∫abItdt. It becomes

∫abItdt=∫abQ'tdt

By using the Net Change Theorem,

∫abQ'tdt=Qb-Qa

∫abItdt=Qb-Qa

The integral ∫abItdt represents the change in the charge from time b to a.

**Conclusion:**

Therefore, ∫abItdt represents the change in the charge from time t= b to t= a.