Someone has a proof that the anti-derivative of a piecewise function does not exist
Subject: Someone has a proof that the anti-derivative of a piecewise function does not exist
From: Richard Hennessy
Date: Thu, 23 Dec 2010 22:22:42 -0500
I found this on the web.
http://www.mathhelpforum.com/math-help/f6/showing-there-no-anti-derivative-piecewise-function-154607.html
Curiously the proof is wrong.
display2d:false;
false
load(pw)$
pw([minf,x,0,1,inf],x);
(signum(x)+1)/2+x*(1-signum(x))/2
deltaint(%,x);
-x^2*(2*unit_step(x)-1)/4+x*(2*unit_step(x)-1)/2+x^2/4+x/2
diff(%,x);
-x*(2*unit_step(x)-1)/2+(2*unit_step(x)-1)/2+x/2+1/2
pwsimp(%,x,'list);
[minf,x,0,0,0,1,inf]