Calculating Average Temperature Using Integrals

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SUMMARY

The average temperature in a city from 9 am to 9 pm can be calculated using the integral of the function T(t) = 50 + 14 sin(πt / 12). The correct limits for the integral are from a = 9 to b = 21, representing the 12-hour period in 24-hour notation. The initial confusion regarding the upper limit being 10 instead of 21 was clarified, emphasizing the importance of correctly setting the limits for accurate results. The integral should be computed as Int[50 + 14 sin(πt / 12), t, 9, 21] to find the average temperature over the specified period.

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A certain city, the temp in degrees Farenheit, t hrs after 9 am was modeled by the function: T(t)=50 + 14 sin (Pi t / 12)
Find avg temp during the period from 9 am to 9 pm.

What i did was take the Int[50 + 14 sin (Pi t / 12),t,0,9]... but this doesn't produce the answer. It says model after 9 am so at 9=0 for a , b = 10 for 9pm?
Any help?
 
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shouldnt b be 12 and not 10 since it is 12 hours from 9am - 9pm
 
Set your limits a,b to a = 9 and b = 21 (using 24-hr notation)
 
i tried 9 to 21 and it didnt work before...
 
it works from 0 to 12, thanks, don't know why i thought 10 DUH
 

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