What Does the Integral of a Child's Growth Rate Represent?

[karush]

If ${w}^{’} \left(t\right)$ is the rate of growth of a child in pounds per year, what does $\int_{5}^{10} {w}^{’}\left(t\right)dt$ represent?

 

[MarkFL]

Given that:

\(\displaystyle dw=w'(t)\,dt\)

Then the integral becomes (exchanging one dummy variable for another):

\(\displaystyle \int_{w(5)}^{w(10)}\,du=w(10)-w(5)\)

So, what does that represent?

 

[karush]

The increase in the child's weigh lbs between the ages of 5 & 10

 

[MarkFL]

The increase in the child's weigh lbs between the ages of 5 & 10

Yes, that's correct. (Yes)