Question

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?

Answer 1

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
=220.17

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