Tutorial Exercise In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 45 + 20 sin Find the average temperature Tave during the period from 9 AM to 9 PM.
Tutorial Exercise In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 45 + 20 sin Find the average temperature Tave during the period from 9 AM to 9 PM.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise
In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function
T(t) = 45 + 20 sin t
12
Find the average temperature Tave during the period from 9 AM to 9 PM.
Step 1
Let 9:00 AM correspond to t = 0 hours. Then, 9:00 PM corresponds to t = 12
12 hours.
Step 2
1
12
12
We must find T
ave
(45 + 20 sin
dt.
12
12
Step 3
Using properties of the integral, we know the following.
r12
r12
r12
45 + 20 sin
sin
dt
=
45 dt + 20
By evaluating the first integral, we get
12
112
45 dt =|45t
45t
= 540
540
Step 4
12
t
dt can be done with the substitution u =
12
t
and
12
The second integral 20
sin
du =
12
dt.
12](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39d48593-4bc5-46a1-a9ce-661c683f5af7%2Fe9383a44-2a13-4cf9-b272-8e12ffb25fb6%2Flpylwy_processed.png&w=3840&q=75)
Transcribed Image Text:This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.
Tutorial Exercise
In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function
T(t) = 45 + 20 sin t
12
Find the average temperature Tave during the period from 9 AM to 9 PM.
Step 1
Let 9:00 AM correspond to t = 0 hours. Then, 9:00 PM corresponds to t = 12
12 hours.
Step 2
1
12
12
We must find T
ave
(45 + 20 sin
dt.
12
12
Step 3
Using properties of the integral, we know the following.
r12
r12
r12
45 + 20 sin
sin
dt
=
45 dt + 20
By evaluating the first integral, we get
12
112
45 dt =|45t
45t
= 540
540
Step 4
12
t
dt can be done with the substitution u =
12
t
and
12
The second integral 20
sin
du =
12
dt.
12
![Step 4
"12
nt
The second integral 20
t
sin
dt can be done with the substitution u =
and
12
du =
12
dt.
12
Step 5
With this substitution, the integration limits change from t = 0 to u =
ol and fromt = 12 to
u = Tt
Step 6
•12
Now, 20
sin
t
dt = 20
sin(u) du.
Jo
Submit
Skip (you cannot come back).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F39d48593-4bc5-46a1-a9ce-661c683f5af7%2Fe9383a44-2a13-4cf9-b272-8e12ffb25fb6%2F327zo5_processed.png&w=3840&q=75)
Transcribed Image Text:Step 4
"12
nt
The second integral 20
t
sin
dt can be done with the substitution u =
and
12
du =
12
dt.
12
Step 5
With this substitution, the integration limits change from t = 0 to u =
ol and fromt = 12 to
u = Tt
Step 6
•12
Now, 20
sin
t
dt = 20
sin(u) du.
Jo
Submit
Skip (you cannot come back).
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