Explanation:
It is given that, the temperature in Gotham in degrees Fahrenheit (°F) t hours after 9 AM be modeled by the function as :
[tex]F(t)=50+15\ sin(\dfrac{\pi t}{12})[/tex]
We need to find the average value of F from t = 0 to t = 12 s
The average value of an integral over and interval a to b is given by :
[tex]f(c)=\dfrac{\int\limits^a_b {f(x).dx}}{b-a}[/tex]
[tex]F(t)=\dfrac{1}{12}{\int\limits^{12}_{0} {50+15\ sin(\dfrac{\pi t}{12}).dt}}[/tex]
Using online calculator, the integral is given by :
[tex]F_{avg}=\dfrac{60\pi +360}{12\pi}[/tex]
[tex]F_{avg}=14.54^{\circ}F[/tex]
So, the average value of From t = 0 to t = 12 s is 14.54 degrees Fahrenheit. Hence, this is the required solution.
