Use Simpson’s Rule to approximate the average value of the temperature function

for a 365-day year. This is one way to estimate the annual mean air temperature in Fairbanks, Alaska. The National Weather Service’s official figure, a numerical average of the daily normal mean air temperatures for the year, is 25.7°F, which is slightly higher than the average value of ƒ(x).

f(x) = 37 sin 2 (x 365 101) + 25