In a certain city the temperature (in °F) e hours after 9 AM was modeled by the function TG) = 49 + 12 sin(). Find the average temperature T during the period from 9 AM to 9 PM.
In a certain city the temperature (in °F) e hours after 9 AM was modeled by the function TG) = 49 + 12 sin(). Find the average temperature T during the period from 9 AM to 9 PM.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function
T(t) = 49 + 12 sin
Find the average temperature T
during the period from 9 AM to 9 PM.
ave
Step 1
Let 9:00 AM correspond to t = 0 hours. Then, 9:00 PM corresponds to t = 12
12 hours.
Step 2
12
49 + 12 sin
12
We must findT
ave
dt.
12
12 - 0
Step 3
Using properties of the integral, we know the following.
12
12
(49+ 12 sin(플) )dt =
49 dt + 12
dt
By evaluating the first integral, we get
12
12ך
49 dt = 49(12 –0)
49t
588
588
Step 4
The second integral 12 " sin
dt can be done with the substitution u =
12
and
du =
12
dt.
Step 5
With this substitution, the integration limits change from t = 0 to u =
and from t = 12 to
Enter an exact number.
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