Daniel Lakeland <dlakelan <at> street-artists.org> writes:
>
>
> Today I was playing around with the concept of absolute integrability:
>
> integrate(sin(x)/x,x,0,inf) gives %pi/2
>
> integrate(abs(sin(x)/x),x,0,inf) asks the seemingly stupid question:
>
> Is ind positive, negative, or zero?
>
> the user has absolutely no idea what maxima is asking... I'm going to
> assume that it has something to do with a change of variable deep
> within the integrator... but it's completely opaque to me.
>
> Any suggestions? I can file a bug if necessary but I'd like to flesh
> out what the bug should say
>
I tried this with mathematica and it gives a wrong result too. Perhaps a
possible solution for this cases would be to compare this with
integrate(sin(x)^2/x,0,inf) that diverges, 0 <= sin(x)^2 <= abs(sin(x)).
Maxima don't know how to compute that integral:
(%i6) integrate(sin(x)^2/x,x,1,inf);
(%o6) integrate(sin(x)^2/x,x,1,inf)
But it can do it by the laplace transform:
(%i19) laplace(sin(t)^2/t,t,s);
Is s positive, negative, or zero?p;
(%o19) 2*(log(s^2+4)/8-log(s)/4)
(%i20) limit(%,s,0);Is s positive or negative?p;
(%o20) und
The above limit is wrong, it should be -inf. So
integrate(abs(sin(x))/x,0,inf)diverges.
I think that there is a long life for mathematician, just not to be replaced
by a computer program :).
Best wishes to the list.