Garbage in garbage out, though, in this case. The integral does not exist, and can't even be thought of as an extended real number like oo.
You can think of sin(oo) and cos(oo) as representing some kind of set of limit points on [-1, 1]. In that case, you can see that the limit points of Integral(sin(x), (x, 0, a)) wrt a are also [-1, 1], because 1 - cos(oo) gives that set. Probably this formalism will break down at some point, because it's not actually what sin(oo) is trying to represent, but it's interesting to note that it works in at least this case. Aaron Meurer On Sat, Jul 6, 2013 at 12:31 PM, someone <[email protected]> wrote: > > > In [2]: integrate( sin(x),(x,0,oo)) > > Out[2]: 1 - cos(∞) > > > > Is such a result acceptable? > > No, it is not. Or at least I'd not. > > What is cos(oo)? The limit of cos(x) > for x-->oo is undefined. One could assign > the interval [-1,1] to cos(oo) but this > does not really help. > > The result above occurs because sympy > blindly uses the fundamental theorem. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > For more options, visit https://groups.google.com/groups/opt_out. > > > -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sympy. For more options, visit https://groups.google.com/groups/opt_out.
