#### To determine

**To represent:**

What does ∫510w'tdt represent.

#### Answer

The change in child’s weight in pounds from the age 5 to the age 10.

#### Explanation

**1) Concept:**

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

∫abF'xdx=Fb-Fa

**2) Given:**

∫510w'(t)dt

3) **Calculation:**

Consider the integral,

*∫510w'tdt;w't* representsthe rate of growth of a child in pounds per year.

By using the Net Change theorem,

∫510w'(t)dt=w10-w(5)

The integral ∫510w'(t)dt represents the net change in a child’s weight between the age 10 and age 5.

**Conclusion:**

Therefore, integral ∫510w'(t)dt represent the net change in child’s weight in pounds between the age 10 and age 5.