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

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SUMMARY

The integral $\int_{5}^{10} {w}^{’}\left(t\right)dt$ represents the total increase in a child's weight between the ages of 5 and 10 years. This is derived from the relationship between the growth rate ${w}^{’}(t)$ and the weight function $w(t)$, where the integral calculates the difference $w(10) - w(5)$. Thus, it quantifies the change in weight over that specific age interval in pounds.

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  • Familiarity with the concept of growth rates in mathematical terms.
  • Knowledge of the relationship between a function and its integral.
  • Basic understanding of weight measurement in pounds.
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karush
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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?
 
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Given that:

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

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

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

So, what does that represent?
 
The increase in the child's weigh lbs between the ages of 5 & 10
 
karush said:
The increase in the child's weigh lbs between the ages of 5 & 10

Yes, that's correct. (Yes)
 

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