Answer:
Average temperature is [tex]43.49^{o}F[/tex]
Step-by-step explanation:
It is given that
[tex]T(t)=40+11sin(\pi t)[/tex]
Thus the average value of the function can be found as
[tex]\overline{T}=\frac{\int_{t_{1}}^{t_{2}}T(t)dt}{t_{2}-t_{1}}[/tex]
Applying values we get
[tex]\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[/tex]
