How to find the integral of a vector on matlab, the solution of which gives a single point?

@jeancheny, @Medhat Elsahookie,@amar kahouadji, @abdelhalim abdelnaplir zekry

There are two main interpretations of finding the integral of a vector in MATLAB that results in a single point:

1. Sum of the vector elements:

The most common way to interpret this scenario is that you want to find the sum of all the elements in the vector. This essentially calculates the total area under the curve if the vector represents a discrete function.

Here's how you can achieve this in MATLAB:

• Using sum function:

Matlab

vector = [1, 2, 3, 4, 5]; integral_value = sum(vector); disp(['The sum (integral) of the vector elements: ', num2str(integral_value)]);

Use code with caution.

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• Using vectorized addition:

Matlab

vector = [1, 2, 3, 4, 5]; integral_value = sum(vector(:)); % Colon expands the vector for summation disp(['The sum (integral) of the vector elements: ', num2str(integral_value)]);

Use code with caution.

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2. Numerical integration for specific functions:

If your vector represents a function evaluated at different points, you can use numerical integration techniques to find the definite integral over a specific interval. MATLAB provides functions like trapz and quad for numerical integration.

Here's an example using trapz for a predefined function:

Matlab

% Define the function (replace with your actual function) f = @(x) sin(x); % Define the integration interval a = 0; b = pi; % Sample the function at points within the interval (optional for trapz) x = linspace(a, b, 100); % 100 points between a and b % Perform numerical integration integral_value = trapz(x, f(x)); disp(['The approximate integral of the function: ', num2str(integral_value)]);

Use code with caution.

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Important points:

• In the second case, ensure your vector represents function evaluations and the integration limits are defined appropriately.
• Numerical integration techniques provide an approximation, and the accuracy depends on the chosen method and the number of samples used.