% Integration by Trapezoidal method % This example shows how you can do numerical integration by Trapizoidal % method % The formula for this method is given as ... % $$ \int\limits_0^{\frac{2\pi}{\omega}}f(t)dt = \frac{h}{2}\left[f(a) + % 2\sum_{i = 0}^{i = K - 1}f(x) + f(b)\right]$ % % where a = lower limit of integration, b = upper limit of integration % % $h = \frac{a - b}{K}$, where K = no. intervals under consideration % Here the function is $ f(t) = \frac{1}{1+x^2} $ Here we are integrating % from 0 to 6, taking 6 % intervals in between. clc; clear all; a = 0; b = 6; K = 6; h = (b - a) / K; t = 0 : .0001 :6; f = inline('1./(1+t.^2)', 't') plot(t, f(t),'r','linewidth',2.5) hold; t1 = a : h : b; stem(t1, f(t1),'m','filled','linewidth',2.5) grid; out = 0; for i = 1 : K - 1 out = out + f(a+i*h); end result = (h / 2) * (f (a) + 2 * (out) + f(b))Thank You

## Monday, April 8, 2013

### Numerical Integraion Using Trapezoidal Rule.

The process of evaluating a definite integral from a set of tabulated values of integrand f(t) is called numerical integration. The following MATLAB code gives a generalized illustration of numerical integration using Trapezoidal rule. The algorithm for the same is given in the comments at the beginning of the program. Try it for your own function.

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