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Recorded data indicates that on a recent date t hours past midnight, the temperature at Logan airport was

f(t) = 14sin(1/3t-2) + 60
degrees Fahrenheit. What was the average temperature between 9 am and noon?

  • Calculus-parentheses -

    f(t) = 14sin(t/3-2) + 60
    ∫f(t)dt from 9 to 12
    =[ 60*t-42*cos(t/3-2) ] from 9 to 12

    Average temperature over 3 hours
    = 220.17/3
    = 73.4°

    Note to Aviana:
    in the absence of parentheses, multiplications and divisions are performed before additions and subtractions.

    Even when 14sin(1/3t-2) + 60 is interpreted correctly as 4sin(t/3-2) + 60, it is a good idea to insert parentheses to emphasize the intention, such as : 4sin((1/3)t-2) + 60

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