Is my approach true to find the area by using 'trapz'?

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Moj 2014-12-13

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评论： Roger Stafford 2014-12-13

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Dear community,

I want to determine s1 and s2 areas which are surrounded by these two plots (please see the figure).

First, I interpolated these two plots:

theta_00 = 0:1e-6:3.5;
y1 = interp1(theta_0, dtheta,theta_00, 'spline');
y2 = interp1(theta_0, dtheta_2, theta_00, 'spline');

in the second place, I used 'fzero' to find the roots:

fun = @(x) interp1(theta_00, (y1 - y2) , x,'spline');
x1 = fzero(fun,[0 1])   % finding roots of fun which is interpolated.
x2 = fzero(fun,[1 2])
x3 = fzero(fun,[2 3])

and now I want to determine these s1 and s2 areas, my problem here. I used 'trapz' like this, but I do not know am I calculating the right values of s1 and s2 ?

 theta_00 = x1:1e-6:x2;
y1 = interp1(theta_0, dtheta,theta_00, 'spline');
y2 = interp1(theta_0, dtheta_2, theta_00, 'spline');
area_1 =  trapz(theta_00,y1)- trapz(theta_00,y2)
theta_00 = x2:1e-6:x3;
y1 = interp1(theta_0, dtheta,theta_00, 'spline');
y2 = interp1(theta_0, dtheta_2, theta_00, 'spline');
area_2 =  trapz(theta_00,y1)- trapz(theta_00,y2)