8 the temperature t at the wall of a furnace varies periodically day a

Question

.8. The temperature T at the wall of a furnace varies periodically day as T(t)=125+50 \sin \frac{2 \pi}{24}(t-6) where t is the time in hours measured from midnight and T is in °C.The ambient temperature T, is 25°C, and the surface area A of the wall is 10 m?. If the heat transfer coefficient h is given as 20 W/m²°C,the heat transfer from the wall is given by ſ[T(t) – T, ]hA dt. Using the trapezoidal rule, compute this integral as accurately as possible for the time interval t = 6 to t = 12. Also evaluate the integral analytically and compare the result with the computed value. Use the quad function in MATLAB to verify the results obtained.-