The furnace in a home consumes heating oil during a particular month at a rate modeled by the function F given by F(t)=0.3+0.1 t-0.85 cos left(frac{2 pi}{15}(t+5)right), where F(t) is measured in gallons per day and t is the number of days since the start of the month. How many gallons of oil does the furnace consume during the first 14 days of the month (from t=0 to t=14) ?

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Step:1 ：Integrate the function F(t) with respect to t from 0 to 14: (int_{0}^{14} (0.1t - 0.85cos(frac{2pi}{15}(t + frac{10}{3})) + 0.3) dt)Step:2 ：Evaluate the integral and simplify the result: (boxed{14}) gallons of oil

Answer

Step: 1 ：Integrate the function F(t) with respect to t from 0 to 14: (int_{0}^{14} (0.1t - 0.85cos(frac{2pi}{15}(t + frac{10}{3})) + 0.3) dt)Step: 2 ：Evaluate the integral and simplify the result: (boxed{14}) gallons of oil

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