Curve Fitting for Integration

The data shown in the following spreadsheet represent the rate of evolution of COj and the take-up rate of Oj during a fermentation reaction. It is important in the study of fermentation processes to obtain the net amount of these gases used and released. This is accomplished by integrating the rates over time. The fourth and fifth columns in the spreadsheet show the results of integrating the data using the trapezoidal rule, and the results are 

In this case, h is fixed by the available experimental data. 

Time(h) CO2 Rate (g/h) O2 Rate (g/h) Trap CO, Trap 0, CO, Evol 0,Evol 

Upon integrating these equations from t = 140 to t = 150, there results (see columns 6 and 7 of the spreadsheet) 

These results compare favorably with those obtained from the trapezoidal rule. 

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