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

  • Context: MHB 
  • Thread starter Thread starter karush
  • Start date Start date
  • Tags Tags
    Change Theorem
Click For Summary

Discussion Overview

The discussion revolves around the interpretation of the integral of a child's growth rate, specifically focusing on the mathematical expression $\int_{5}^{10} {w}^{’}\left(t\right)dt$ and what it signifies in the context of a child's weight over a specified age range.

Discussion Character

  • Exploratory, Mathematical reasoning

Main Points Raised

  • One participant asks what the integral $\int_{5}^{10} {w}^{’}\left(t\right)dt$ represents in terms of a child's growth rate.
  • Another participant provides a mathematical transformation of the integral, suggesting that it can be expressed as $w(10) - w(5)$.
  • Some participants propose that this expression represents the increase in the child's weight in pounds between the ages of 5 and 10.
  • A later reply confirms the interpretation of the integral as the increase in the child's weight between the ages of 5 and 10.

Areas of Agreement / Disagreement

There appears to be agreement among participants regarding the interpretation of the integral as representing the increase in the child's weight between the ages of 5 and 10, although the initial question remains open to further exploration.

Contextual Notes

The discussion does not address potential limitations or assumptions related to the growth rate or the context of the integral.

karush
Gold Member
MHB
Messages
3,240
Reaction score
5
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?
 
Last edited:
Physics news on Phys.org
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)
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 20 ·
Replies
20
Views
4K