numerical integration rectangle in matlab

To perform numerical integration using the rectangle method in MATLAB, one can follow the following algorithm:

1. Define the function to integrate, f(x).
2. Define the limits of integration, a and b.
3. Choose the number of rectangular subintervals, N, to divide the integration interval.
4. Calculate the width of the subintervals, h = (b-a)/N.
5. Define a variable to store the numerical approximation of the integral, approx.
6. Use a for loop to perform the approximation for each subinterval, i.e. approximating the area of the i-th rectangle as f(a+i*h)*h.
7. Sum up the areas of all rectangles to obtain the total approximation, approx.

Below is an implementation of the rectangle method for numerical integration in MATLAB:

main.m
% Define function to integrate
f = @(x) exp(-x.^2);

% Define limits of integration
a = 0;
b = 1;

% Choose number of subintervals
N = 100;

% Calculate width of subintervals
h = (b-a)/N;

% Initialize approximation variable
approx = 0;

% Perform approximation using a for loop
for i = 1:N
    approx = approx + f(a+i*h)*h;
end

% Display the numerical approximation
fprintf('Numerical approximation: %.5f\n', approx);
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In the above implementation, we have used the exponential function as an example function to integrate. One can replace that with any function of choice. The numerical approximation is displayed using the fprintf function. The argument %.5f specifies displaying the floating-point number with 5 decimal places.