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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
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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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 |×
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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