Chapter 7.7, Problem 30E

Temperature data Hourly temperature data for Boulder, Colorado. San Francisco, California. Nantucket, Massachusetts, and Duluth, Minnesota, over a 12 hr period on the same day of January are shown in the figure. Assume that these data are taken from a continuous temperature function T(t). The average temperature over the 12-hr period is $\bar{T}=\frac{1}{12}{\displaystyle {\int }_0^{12}T(t)dt}$.

30. Find an accurate approximation to the average temperature over the 12-hr period for Duluth. State your method.