Summary of Newton-Cotes Integration

The three Newton-Cotes formulas of integration derived in the previous sections are summarized in Table 4.4. 

In the derivation of the Newton-Cotes formulas, the function y = f(x) is approximated by the Gregory-Newton polynomial Pjix) of degree n with remainder R x). The evaluation of the integral is performed  

There are three functions in MATLAB, trapz.m, quad.m, and quadS.m, that numerically evaluate the integral of a vector or a function using different Newton-Cotes formulas  

Example 4.3 Integration formulas-Trapezoidal and Simpson s 1/3 Rules. Write a general MATLAB function for integrating experimental data using Simpson s 1/3 rule. Compare the results of this function and the existing MATLAB function trapz (trapezoidal rule) for solution of the following problem  

Using Simp.son s 1/3 rule, calculate the total amounts of carbon dioxide produced and oxygen consumed during this 10-h period of fermentation. Repeal this using the trapezoidal rule and compare the results obtained from the two methods. 

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