Games with integrate, infinity, symmetry, wxmaxima 0.7.1
Subject: Games with integrate, infinity, symmetry, wxmaxima 0.7.1
From: Richard Fateman
Date: Sat, 7 Jul 2007 11:07:31 -0700
R:='integrate(sinh(x),x,-inf,inf)
R,integrate; says principal value, 0. That's good.
If you change the variable, eg. changevar(R,x=t+1,t,x) you get
integrate(sinh(t+1),t,-inf-1,inf); I would hope to simplify -inf-1 to
-inf, and there is a program, namely limit that does it. Limit(-inf-1) -->
inf.
However, limit ( the_integral...) doesn't do the job. That is, the -inf-1
in the lower limit stays there.
But the integral from -inf to inf of sinh(t+1) diverges. Maybe this is the
right math answer?
For what it is worth, Mathematica 6.0 does not get R above, correct, even if
you say to find Principal Value.
RJF