Calculus II Average Value of a Function

Question

In a certain city the temperature (in degrees Fahrenheit)  hours after 9am was approximated by the function: T(t)=80+11sin(πt/12)

a) Determine the temperature at 9am

b) Determine the temperature at 3pm

c) Find the average temperature during the period 9am-9pm

Answer 1

To solve (a) and (b) you need to plug into your equation, but be careful! You are are not plugging in 9 and 3 - the problem specifies that t is the number of hours after 9am. This means for instance that 10am would be t=1. To find average value you need to use the average value formula: 1/(b-a) ∫T(t)dt. If you are doing this math by hand you will need to evaluate the integral from a to b using antidifferentiation.