right sum rectangular rule in matlab

The summation or rectangular rule method for numerical integration is a simple numerical method that approximates the definite integral of a function by dividing the area under the function into a series of rectangles. The area of each rectangle is the function value at the midpoint of the rectangle multiplied by the width of the rectangle. The sum of the areas of all the rectangles gives an approximation of the definite integral of the function.

To implement the rectangular rule in MATLAB, we will define a function that takes the function to be integrated, the limits of integration, and the number of rectangles as input parameters.

main.m
function I = rectangular_rule(f, a, b, n)
% This function implements the rectangular rule for numerical integration
% of the function f over the interval [a,b] using n rectangles.

% Compute the width of each rectangle
h = (b - a) / n;

% Compute the sum of the areas of all the rectangles
x = linspace(a + h/2, b - h/2, n);
I = sum(f(x) * h);
end
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In this implementation, we first compute the width of each rectangle h using the formula h = (b - a) / n. We then compute the midpoint of each rectangle x using the linspace function. Finally, we compute the sum of the areas of all the rectangles by evaluating the function at each midpoint f(x) and multiplying by the width of the rectangle h. This sum is returned as the approximate value of the definite integral.