How to calculate the area between two curves separately based on being below or above.

Hi Alll

how can I seperate calculate all the area difference when the orange line is below the black line and vice versa. In other words, calculating A1 and A3 seprately from A2.

Thanks

[Austin Thai]

What does your data look like? Are these curves analytic functions or discrete datapoints? Are they equally spaced in x?

Answer 1

[Star Strider]

Try something like this:

t = linspace(0, 10*pi, 500);                                    % Create Data
y1 = exp(-0.1*t) .* sin(t);                                     % Create Data
y2 = exp(-0.2*t) .* cos(t);                                     % Create Data

icptidx = find(diff(sign(y1 - y2)));                            % Approximate Indices Of Intersections
icptidx = [1, icptidx, numel(t)]; 

areavct = cumtrapz(t, y1 - y2);                                 % Cumulative Areas

for k = 1:numel(icptidx)-1
    areas(k) = areavct(icptidx(k+1)) - areavct(icptidx(k));
    xtxt(k) = (t(icptidx(k+1))+t(icptidx(k)))/2;                % Used in ‘text’ To Label Areas
    ytxt(k) = (y1(icptidx(k+1))+y2(icptidx(k)))/2;              % Used in ‘text’ To Label Areas
end

figure
plot(t, y1)
hold on
plot(t,y2)
hold off
grid
text(xtxt, ytxt, compose('$\\leftarrow Area = %.3f$', areas), 'Interpreter','latex', 'Rotation',60)
ylim([min(ylim) max(ylim)+0.2])

.