For those interested in correctness of evaluating this integral in pw.mac.
There is an easy way to get rid of the discontinuity of the antidiff() using
pw.mac functions (at least in this case). You can't use the function
continuousp() that I wrote to verify it because limit causes a bind stack
overflow in this case. You can plot it and it looks continuous, but that is
about the only way to tell that I know of without resorting to another CAS.
(%i14) integrate(exp(-x^4),x);
(%o14) -gamma_incomplete(1/4,x^4)*x/(4*abs(x))
(%i15)
F(x):=''(ratsimp(zerospikes(pw(pwsimp(linearize(abs2signum(%)),x,'list),x,'connect))));
(%o15)
F(x):=-((gamma_incomplete(1/4,x^4)-gamma(1/4))*signum(x)-gamma(1/4))/4
Now you can use integrate(exp(-x^4),x,a,b) = F(b)-F(a).
Rich
-----Original Message-----
From: Richard Hennessy
Sent: Tuesday, January 03, 2012 8:31 PM
To: Barton Willis
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] Bug in limit or integrate
(%i10) continuousp(abs(x),x,0);
(%o10) true
(%i11) continuousp(abs(x)^2,x,0);
(%o11) true
(%i12) continuousp(1/abs(x-a),x,a);
expt: undefined: 0 to a negative exponent.
(%o12) false
(%i13) continuousp(1/(x-a),x,a);
(%o13) false
(%i14) continuousp(1/(x-a)^3,x,a);
(%o14) false
(%i15) continuousp(1/(sqrt(x-a))^3,x,a);
Rich