trapezium rule in matlab

To implement the trapezium rule in MATLAB, you can follow these steps:

1. Define the function you want to integrate. Let's say your function is f(x).

2. Specify the interval over which you want to integrate. Let's say your interval is from a to b.

3. Determine the number of sub-intervals n to divide the interval into. The more sub-intervals you use, the more accurate your approximation will be.

4. Calculate the width of each sub-interval h, which is given by h = (b - a) / n.

5. Create an array of n+1 equally spaced points within the interval [a, b] using the linspace function. Let's call this array x.

main.m
x = linspace(a, b, n+1);
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6. Evaluate the function f(x) at each point in x. Let's call this array y.

main.m
y = f(x);
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7. Apply the trapezium rule formula to calculate the approximate integral I:

main.m
I = (h / 2) * (y(1) + 2*sum(y(2:end-1)) + y(end));
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8. Display the result:

main.m
disp(I);
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Here's a complete example code snippet for the trapezium rule in MATLAB:

main.m
f = @(x) cos(x); % Define the function f(x)
a = 0; % Lower bound of the interval
b = pi; % Upper bound of the interval
n = 100; % Number of sub-intervals
h = (b - a) / n; % Width of each sub-interval

x = linspace(a, b, n+1); % Create equally spaced points
y = f(x); % Evaluate the function at each point

I = (h / 2) * (y(1) + 2*sum(y(2:end-1)) + y(end)); % Trapezium rule formula
disp(I); % Display the result
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This code snippet will approximate the integral of cos(x) from 0 to pi using 100 sub-intervals.

Please note that the accuracy of the trapezium rule depends on the number of sub-intervals used. Increasing the value of n will improve the approximation.