Basic Idea of Numerical Integration

The basic idea of the numerical integration is to approximate the function y x) by a polynomial of degree N, and then to perform the integration of this 

If the function y(jc) is known, we simply choose discrete positions x (for example, 2, 3, or 4 points) within the domain of integration (a x b) and then cause an approximating polynomial to pass through these points. We can then perform the integration of the approximating polynomial. If the discrete points are unequally spaced, the Lagrange polynomial developed in Chapter 8 can be used to fit the data, white if the points are equally spaced the Newton 

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While there is an analytical solution for this mechanism, the formula for the calculation of the concentration profiles for A and B is fairly complex, involving the tan and atan functions (according to Matlab s symbolic toolbox). We use it to demonstrate the basic ideas of numerical integration. 

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