   Chapter 4.5, Problem 58E

Chapter
Section
Textbook Problem

# A model for the basal metabolism rate, in kcal/h, of a young man is R ( t ) = 85 − 0.18 cos ( π t / 12 ) , where t is the time in hours measured from 5:00 am. What is this man’s total basal metabolism, ∫ 0 24 R ( t ) d t , over a 24-hour time period?

To determine

To find:

The man’s total basal metabolism over an 24- hour time period

Explanation

1) Concept:

i. The substitution rule:

If u=g(x) is a differentiable function whose range is I and f is continuous on I, then f(gx)g'xdx=f(u)du. Here,g(x) is substituted as u and g(x)dx =du.

ii. Indefinite integral

xn dx=xn+1n+1+C   (n-1)

2) Given:

The basal metabolism rate of man is Rt=85-0.18cosπt12.

3) Calculation:

Given that the basal metabolism rate of man is Rt=85-0.18cosπt12

To find the man’s total basal metabolism over an 24- hour time period, we need to integrate the rate of basal metabolism of man over 0 to 24.

024Rtdt=02485-0.18cosπt12dt

Use the substitution method.

Substitute πt12=u

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