rectangular rule to solve an integral in matlab

The rectangular rule is a numerical method used to approximate the value of integrals. Here's how to implement the rectangular rule in MATLAB:

main.m
% define the function to be integrated
f = @(x) sin(x);

% define the limits of integration
a = 0;
b = pi/2;

% define the number of rectangles (interval size)
n = 100;

% calculate the width of each rectangle
dx = (b-a)/n;

% evaluate the function at the midpoints of each rectangle
x = linspace(a+dx/2,b-dx/2,n);
y = f(x);

% calculate the area of each rectangle
area = dx*y;

% sum up the areas of all the rectangles to get the final approximation
approximation = sum(area);
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In this example, we're integrating the function f(x) = sin(x) over the interval [0, pi/2]. We're using n=100 rectangles to approximate the area under the curve.

Note that we've defined f as a function handle, which allows us to evaluate the function at multiple points simultaneously using y = f(x).

The width of each rectangle is calculated as dx = (b-a)/n. We then use linspace to generate an array of midpoints x for each rectangle, and evaluate the function at those points to get an array of function values y.

Finally, we calculate the area of each rectangle by multiplying the width dx by the corresponding function value y, and sum up all the areas to get the final approximation.