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Math Help - integration: finding the average value of a funciton

  1. #1
    sss
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    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.
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    Quote Originally Posted by sss View Post
    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.
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