In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 46 + 17 sin(πt/12) .

Question

In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function

T(t) = 46 + 17 sin(πt/12)

.

Find the average temperature T_ave during the period from 9 AM to 9 PM. (Round your answer to the nearest whole number.)

Answer 1

The average you are looking for is 46 + (17/12)∫sin(πt/12) dt between 0 and 12.

If you cannot compute that integral, please make a comment to that effect and I will help you further.