If you scale the curve in the X direction by a factor of 2, then scale the curve in Y by a factor of 1/2.
X = 0:100; % linear x
Y = rand(1,101); % random y
plot(X,Y)
A1x = trapz(X,Y) % area under the curve
A2x = trapz(2*X,Y) % area under the curve when X is stretched by 2
A2xc = trapz(2*X,Y/2) % corrected
Ignoring trying to intuit the calculus, it's easier to look at this in relative terms. Consider the curve occupying a rectangular box, wherein the area under the curve (Ac) occupies some fraction of the total area (At) of the box. If you scale one dimension of the box (and everything therein) by 2, the total area is doubled, but the area ratio remains constant. In other words, Ac is simply proportional to At.
If there's something other than a simple scale transformation going on (e.g. changing data extents), that may not hold true.
