how to visualize integrals in matlab

To visualize integrals in Matlab, you can use the following approaches:

1. Numerical Integration with `quad` function

You can use the quad function to numerically evaluate definite integrals.


main.m
% Define the integrand function
f = @(x) x.^2;

% Define the limits of integration
a = 0;
b = 2;

% Numerically evaluate the integral
result = quad(f, a, b);
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2. Visualizing the Integral using `plot` function

To visualize the integral, you can plot the area under the curve using the plot function.


main.m
% Define the x-values
x = linspace(0, 2, 100);

% Define the integrand function
f = @(x) x.^2;

% Evaluate the function at x-values
y = f(x);

% Plot the function
plot(x, y);
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3. Filling the Area under the Curve

To fill the area under the curve, you can use the fill function or area function.


main.m
% Define the x-values
x = linspace(0, 2, 100);

% Define the integrand function
f = @(x) x.^2;

% Evaluate the function at x-values
y = f(x);

% Fill the area under the curve
fill(x, y, 'b', 'FaceAlpha', 0.2);
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4. Using `integral` function with `plot` function

You can use the integral function with the plot function to visualize the integral.


main.m
% Define the integrand function
f = @(x) x.^2;

% Define the x-values
x = linspace(0, 2, 100);

% Evaluate the function at x-values
y = f(x);

% Calculate the integral
result = integral(f, 0, 2);

% Plot the function
plot(x, y);
% Fill the area under the curve
fill(x, y, 'b', 'FaceAlpha', 0.2);
% Add text to display the integral value
text(1, 1, sprintf('Integral = %.2f', result));
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