Part 1 Write a general MATLAB function for integrating experimental data using Simpsons 1/3 rule. Your function should check if there are an odd number of intervals, if there are, the trapezoidal rule should be used for the last interval. The first line of your MATLAB function should look like: function I = Simpson(x,y) Where the function numerically evaluates the integral of the vector of function values y with respect to x Your matlab function should also include the following: Error check that the inputs are the same length Error check that the x input is equally spaced Warn the user (not an error, just a warning) if the trapezoidal rule has to be used on the last interval.

Part 2 - FOR TESTING PURPOSES ONLY, DO NOT TURN IN Two important quantities when studying fermentation are the carbon dioxide evolution rate (g/h) and the oxygen uptake rate (g/h). These are calculated from expiremental analysis of the inlet and exit gases of the fermentor, and the flow rates, temperature, and pressure of these gases.

Using your function in part 1, and the data table below, calculate the total amount of carbon dioxide produced and oxygen consumed during fermentation. Compare to the value that the MATLAB function trapz() computes. Time of Fermentation (h) Carbon Dioxide Evolution Rate (g/h) Oxygen Uptake Rate (g/h) 140 15.72 15.49 141 15.53 16.16 142 15.19 15.35 143 16.56 15.13 144 16.21 14.20 145 17.39 14.23 146 17.36 14.29 147 17.42 12.74 148 17.60 14.74 149 17.75 13.68