# Thread: integration: finding the average value of a funciton

1. ## integration: finding the average value of a funciton

In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the function

T(t)=80 + 11 sin(pi*t/12)

Determine the temperature at 9 am.
Determine the temperature at 3 pm.
Find the average temperature during the period from 9 am to 9 pm.

2. Originally Posted by sss
In a certain city the temperature (in degrees Fahrenheit) t hours after 9am was approximated by the function

T(t)=80 + 11 sin(pi*t/12)

Determine the temperature at 9 am. T(0) = ?

Determine the temperature at 3 pm. T(6) = ?

Find the average temperature during the period from 9 am to 9 pm.

$T_{avg} = \frac{1}{12}\int_0^{12} 80 + 11\sin\left(\frac{\pi t}{12}\right) \, dt$
first two questions are just function values of T(t)

last question is set up for you ... give it a try.