Mathematics 134 -- Intensive Calculus for Science 2

Discussion 1 -- Using the Definite Integral

January 22, 2002

Background

The graphs below (taken from problem 28 in Section 5.3 of our text) show the ``height velocity graphs'' of average American boys and girls from age 3 to age 18. This kind of information is often used by doctors to follow the progress of children and determine whether they are growing normally, or whether they might have some growth deficiency (possibly caused by an endocrine disorder).

Discussion Questions

1. One one graph, for instance, at x = 10 years we see that y = 6 cm/year. Say in words what this information means.
2. Which curve is the ``height velocity'' curve for boys and which is the ``height velocity'' curve for girls? Explain how you can tell. (Note: This is not entirely a mathematical question -- you will need to think about the relative growth rates of girls and boys at different ages from your own experience.)
3. About how much does the average girl grow (in cm) between ages 4 and 11? Express your answer as a definite integral, then estimate the value of that integral from the graphs.
4. Find an estimate of the average growth rate of boys between ages 10 and 18 (in cm/yr). First, express your answer using a definite integral, then estimate the value of that integral from the graphs.
5. Assume that average boys and girls are the same height at age 3. How much taller is the average man than the average woman?

Assignment