Use Simpson’s Rule to approximate the av-erage value of the temperature function ƒ(x) = 37 sin (2pai /365 (x - 101)) + 25 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).

Question

Use Simpson’s Rule to approximate the av-erage value of the temperature function

ƒ(x) = 37 sin (2pai /365 (x - 101)) + 25

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).