On 11/11/2010 7:33 AM, Barton Willis wrote:
> How many users will be satisfied with:
>
> (%i1) integrate(sqrt((x^2-2*x+1)/x),x,0,1);
> (%o1) -4/3
>
> (%i2) integrate(sqrt(x-2+1/x),x,0,1);
> (%o2) 4/3
>
> --Barton
>
I'm not sure that this has to do with integration.
sqrt((x^2-2*x+1)/x)
is simplified to sqrt(1/x) * sqrt(x^2-2*x+1)
which is, in general, false.
Proof. Take that "simplified" version and evaluate at %i and you get
-sqrt(2)*%i.
The unsimplified expression can be evaluated at %i by first evaluating
the "radicand"
to yield -2. taking the sqrt give sqrt(2)*%i.
The signs differ, in case you didn't notice.
Just to check if this is something introduced by Maxima hackers:
This same "feature" appears in Macsyma 2.4.0, so no, it's been around
for a while.
RJF