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    integral application

    Im really not sure how to even approach this problem... it says

    Suppose the outdoor temperature on a particular day is given by T(t) = 60 + 16*(sin((pi*t)/24))^2 where time is measured in hours and t =0 corresponds to midnight. What is the average temperature for a 24-hour period?
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    Quote Originally Posted by synnexster View Post
    Im really not sure how to even approach this problem... it says

    Suppose the outdoor temperature on a particular day is given by T(t) = 60 + 16*(sin((pi*t)/24))^2 where time is measured in hours and t =0 corresponds to midnight. What is the average temperature for a 24-hour period?
    There are two ways to approach this depending on what class you are in.

    The first is to simply note that the average of sin^2(\theta) over a full period is 1/2.

    The integral formula is:
    \bar{f(x)} = \frac{1}{X} \int_0^Tdxf(x)
    where X is the interval over which you are integrating.

    So
    \bar{T} = \frac{1}{24} \int_0^{24}dt \left ( 60 + 16*sin \left ( \frac{\pi t}{24} \right )^2 \right )

    I'll leave it to you to do the integration. If you need help, feel free to let me know.

    -Dan
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