Question

In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 40 + 11 sin πt 12 . Find the average temperature Tave during the period from 9 AM to 9 PM. (Round your answer to the nearest whole number.)

Answer 1

Answer:

Average temperature is $43.49^{o}F$

Step-by-step explanation:

It is given that

$T(t)=40+11sin(\pi t)$

Thus the average value of the function can be found as

$\overline{T}=\frac{\int_{t_{1}}^{t_{2}}T(t)dt}{t_{2}-t_{1}}$

Applying values we get

$\overline{T}=\frac{\int_{0}^{12}(40+11sin(\pi t))dt}{12-0}\\\\\overline{T}=\frac{1}{12} (\int_{0}^{12}(40+11sin(\pi t))dt)\\\\\therefore \overline{T}=43.49^{o}F$