In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 45 + 16 sin ?t 12 . Find the average temperature Tave during the period from 9 AM to 9 PM
In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 45 + 16 sin ?t 12 . 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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Question
In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function
T(t) = 45 + 16 sin
.
?t |
12 |
Find the average temperature Tave during the period from 9 AM to 9 PM
![Using properties of the integral, we know the following.
L"(45 + 16 sin) Jer =
12
12
nt
45 dt + 16
dt
sin
By evaluating the first integral, we get
12
45 dt =|45t
45t
or
= 540
540
Step 4
The second integral 16
dt can be done with the substitution u =
t
and du =
dt.
12
12
12
Step 5
With this substitution, the integration limits change fromt = 0 to u =
0 and fromt = 12 to u = T
Step 6
16/" an) at = 14
12
sin
dt = 16 t
sin(u) du.
Step 7
This can be evaluated as
192
192
|×](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe6d7b9ce-d2f0-4e06-b3ff-298d284fb108%2F8caa9072-e53c-4569-b052-fea2aa2d25fd%2Fhthh0li_processed.png&w=3840&q=75)
Transcribed Image Text:Using properties of the integral, we know the following.
L"(45 + 16 sin) Jer =
12
12
nt
45 dt + 16
dt
sin
By evaluating the first integral, we get
12
45 dt =|45t
45t
or
= 540
540
Step 4
The second integral 16
dt can be done with the substitution u =
t
and du =
dt.
12
12
12
Step 5
With this substitution, the integration limits change fromt = 0 to u =
0 and fromt = 12 to u = T
Step 6
16/" an) at = 14
12
sin
dt = 16 t
sin(u) du.
Step 7
This can be evaluated as
192
192
|×
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