# The total basal metabolism rate of a young man. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 5.5, Problem 62E
To determine

## To calculate: The total basal metabolism rate of a young man.

Expert Solution

The total basal metabolism rate of a young man is 2040kcal_.

### Explanation of Solution

Given:

The function is R(t)=850.18cos(πt12).

Show the integral function is,

024R(t)dt=024[850.18cos(πt12)]dt.

The region lies between t=0 and t=24.

Calculation:

Take the consideration as follows:

u=πt12 (1)

Differentiate both sides of the Equation (1).

du=π12dtdt=12πdu

Calculate the lower limit value of u using Equation (1).

Substitute 0 for t in Equation (1).

u=π(0)12=0

Calculate the upper limit value of u using Equation (1).

Substitute 24 for t in Equation (1).

u=π(24)12=2π

The integral function is,

024[850.18cos(πt12)]dt (2)

Apply lower and upper limits for u in Equation (2).

Substitute u for (πt12) and (12πdu) for dt in Equation (2).

024[850.18cos(πt12)]dt=02π(850.18cosu)(12πdu)=12π02π(850.18cosu)du (3)

Integrate Equation (3).

12π02π(850.18cosu)du=12π[85u0.18sinu]02π=12π{[85(2π)0.18sin(2π)][85(0)0.18sin(0)]}=12π[(170π0)(00)]=12π×170π

=2040

Hence, the total basal metabolism rate of the young man is 2040kcal_.

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