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Temperature Profile Plate Dimensions X 1 8 Y E 7 10 Illustrated Figure Temperature Profil Q43789552

The temperature profile on a plate with dimensions (x € (-1,8]) and (y E (-7,10]) is illustrated in the figure below. The temperature profile on the plate is described by: T(x,y) = y sin(x) – x cos(y) where T represents the temperature. The average temperature of the plate can be calculated as: 1 10 8 Taverage = 0 T(x, y) dxdy AJ-7 J-1 where A represents the total surface area of the plate. Temperature y -10 2 0 Q2c In the Q2c.m file, calculate the average temperature of the plate using the comp_simp13() function written in Q2a with the minimum number of points required in each direction (x and y). Continue to increase the number of points until the approximated volume achieves an accuracy of 8 decimal places (DP) matching the temperature value obtained using MATLAB’s integral2() function. Use fprintf to print the number of points, the approximated average temperature, MATLAB’s average temperature value, and the error, but only when the approximated average temperature has improved by at least a decimal place. The error is taken to be the absolute difference between the approximated average temperature and the MATLAB’s integral2() value. An example of this is shown below, with the decimal places bolded and underlined for clarity (you do not need to bold and underline the values in your MATLAB answers). pts X X temp_approx X.XXXXXXXXX X.XXXXXXXXX X.XXXXXXXXX X.XXXXXXXXX temp_MATLAB X.XXXXXXXXX X.XXXXXXXXX X.XXXXXXXXX X.XXXXXXXXX error 0.OXXXXXXXX 0.00XXXXXXX 0.000XXXXXX 0.0000XXXXX $ ܝܙ ܚ ܚ X ܟ Hint: Start by evaluating the inner integral along the x dimension for each value of y. The resulting values can then be integrated along the y dimension. Hint: Look at the result of log10(error) to help determine the number of zeros in the error (i.e. DP). *You should still have four figure windows by the end of this task. comp_simp13_vector.m x untitled x untitled2 Ifunction [ ] = comp_simp13_vector( ). % [ ] = comp_simp13_vector( ) % Written by: ???, ID: ??? % Last modified: ??? % uses midpoint method to solve an ODE % INPUTS: % OUTPUTS: – Show transcribed image text The temperature profile on a plate with dimensions (x € (-1,8]) and (y E (-7,10]) is illustrated in the figure below. The temperature profile on the plate is described by: T(x,y) = y sin(x) – x cos(y) where T represents the temperature. The average temperature of the plate can be calculated as: 1 10 8 Taverage = 0 T(x, y) dxdy AJ-7 J-1 where A represents the total surface area of the plate. Temperature y -10 2 0
Q2c In the Q2c.m file, calculate the average temperature of the plate using the comp_simp13() function written in Q2a with the minimum number of points required in each direction (x and y). Continue to increase the number of points until the approximated volume achieves an accuracy of 8 decimal places (DP) matching the temperature value obtained using MATLAB’s integral2() function. Use fprintf to print the number of points, the approximated average temperature, MATLAB’s average temperature value, and the error, but only when the approximated average temperature has improved by at least a decimal place. The error is taken to be the absolute difference between the approximated average temperature and the MATLAB’s integral2() value. An example of this is shown below, with the decimal places bolded and underlined for clarity (you do not need to bold and underline the values in your MATLAB answers). pts X X temp_approx X.XXXXXXXXX X.XXXXXXXXX X.XXXXXXXXX X.XXXXXXXXX temp_MATLAB X.XXXXXXXXX X.XXXXXXXXX X.XXXXXXXXX X.XXXXXXXXX error 0.OXXXXXXXX 0.00XXXXXXX 0.000XXXXXX 0.0000XXXXX $ ܝܙ ܚ ܚ X ܟ Hint: Start by evaluating the inner integral along the x dimension for each value of y. The resulting values can then be integrated along the y dimension. Hint: Look at the result of log10(error) to help determine the number of zeros in the error (i.e. DP). *You should still have four figure windows by the end of this task.
comp_simp13_vector.m x untitled x untitled2 Ifunction [ ] = comp_simp13_vector( ). % [ ] = comp_simp13_vector( ) % Written by: ???, ID: ??? % Last modified: ??? % uses midpoint method to solve an ODE % INPUTS: % OUTPUTS: –

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Answer to The temperature profile on a plate with dimensions (x € (-1,8]) and (y E (-7,10]) is illustrated in the figure below. …