On 03/17/2013 05:03 PM, David Scherfgen wrote:
> Hello,
>
> can anyone explain this obviously wrong behavior?
>
> (%i1) integrate(sqrt(1-cos(x)^2),x);
> (%o1) cos(x)
> (%i2) trigsimp(sqrt(1-cos(x)^2));
> (%o2) abs(sin(x))
Hi,
I agree with you; the result is wrong in the sense that it does not
agree with other Maxima commands, such as the trigsimp or:
plot2d ( sqrt(1-cos(t)^2), [t,0,3*%pi]);
It would be very nice to get the following result:
(%i1) integrate(sqrt(1-cos(x)^2),x);
(%o1) 2*floor (t / %pi) + 1 -(-1)^( floor (t / %pi)) * cos(t)
but that is not possible with the current version of integrate. On the
other hand, it would also be nice to have:
(%i2) diff (%,t);
(%o2) abs (sin (x))
but those extensions to integrate and diff would need some major work
from someone and I would not recommend that kind of project to someone
who is not very familiar with Maxima internals.
Cheers,
Jaime