In order to obtain the plot shared in the question you can follow the following example:
% Define the range for x, can be adjusted
x = linspace(0, 1, 100);
% For R1, we have to get the Area Under Curve (AUC) of x = y
y = x;
x_fill = [x, fliplr(x)]; % Obtaining arrays to define AUC
y_fill = [y, zeros(size(y))];
x1 = sqrt(sqrt(y_fill)); % AUC for the curve y = x^(1/4)
% Using 'fill' function to plot the AUC
p1 = fill(x_fill, y_fill, 'cyan', 'FaceAlpha', 0.7, 'EdgeColor', 'none');
hold on
p2 = fill(y_fill, x_fill, 'green', 'FaceAlpha', 0.8, 'EdgeColor', 'none');
hold on
p3 = fill(y_fill, x1, [1, 0.5, 0], 'FaceAlpha', 0.9, 'EdgeColor', 'none');
xlabel('x');
ylabel('y');
grid on;
axis equal;
legend([p3, p1, p2], {'R3: y = x^{1/4}', 'R1', 'R2'}, 'Location', 'best');
hold off;
This will give you the desired plot which would look like:
You can refer to the following Mathworks documentation to know more about the 'fill' function:
Hope this resolves your query. Thanks.
