How to calculate the area between two curves

Hi,

How can I calculate the erea between this two curves? (I need the yellow coloured area)

where:

x1 =  [0    1    1.5608    2.4538    2.7360];
y1 =  [0    0   -0.8278   -0.3777   -1.5954];

and

x2 = {vector 14494x1} 
y2 = {vector 14494x1}

All the datas are in the attached Curve.mat file.

Thank you in advance!

[Rik]

What did you try already?

[Paolo Rosettani]

I've tried this:

I used

trapz

for each curve and then subtract them...

but with this way I cannot find the yellow area (in the prevoius figure)

Answer 1

[David Wilson]

Try the following : I've used one of the many interpolation routines, but I notice that you have not sorted your (x2, y2) data, and that you must extrapolate to get the full range.

load curves

x1 =  [0    1    1.5608    2.4538    2.7360];
y1 =  [0    0   -0.8278   -0.3777   -1.5954];

plot(x1, y1, x2, y2)
grid on 

%% Now interpolate x1 to x2 

% sort first (for some strange reason) 
[x2s, idx] = sort(x2, 'ascend'); 
y2s = y2(idx); 


[y1i] = interp1(x1, y1, x2s, 'pchip', 'extrap'); % Assume extrapolation  

subplot(2,1,1); 
plot(x2s, [y1i], '-', x2s, y2s)
ylim([-2, 0.5])

dy = abs([y1i-y2s]); 
A = trapz(x2s,dy)

subplot(2,1,2); 
plot(x2s, abs([y1i-y2s]))
ylabel('|y_1-y_2|')
title(sprintf('Area = %2.3f', A))

[Paolo Rosettani]

Thank you so much!

This solution is perfect :-)