#8624: integral of abs(cos(x))*sin(x) gives false results
-----------------------------+----------------------------------------------
Reporter: jeroen | Owner: burcin
Type: defect | Status: needs_work
Priority: minor | Milestone: sage-4.4.3
Component: calculus | Keywords:
Author: Jason Grout | Upstream: N/A
Reviewer: Burcin Erocal | Merged:
Work_issues: |
-----------------------------+----------------------------------------------
Comment(by kcrisman):
> ----
> {{{
> **********************************************************************
> File ".../devel/sage-t/sage/misc/functional.py", line 705:
> sage: h = integral(sin(x)/x^2, (x, 1, pi/2)); h
> Expected:
> integrate(sin(x)/x^2, x, 1, 1/2*pi)
> Got:
> 1/2*gamma(-1, -1/2*I*pi) + 1/2*gamma(-1, 1/2*I*pi) - 1/2*gamma(-1,
-I) - 1/2*gamma(-1, I)
> **********************************************************************
> File ".../devel/sage-t/sage/misc/functional.py", line 707:
> sage: h.n()
> Expected:
> 0.339447940978915...
> Got:
> 0.339447940978884
> **********************************************************************
> }}}
Hmm, did you have the new Maxima package at #8731 already installed? This
is dealt with there.
>
> Here's the Maple output:
> {{{
> > integrate(sin(x)/x^2, x=1..1/2*Pi);
> memory used=7.6MB, alloc=5.1MB, time=0.33
> Pi
> sin(1) Pi - Ci(1) Pi + Ci(----) Pi - 2
> 2
> --------------------------------------
> Pi
> }}}
>
> It would be interesting to see how this is transformed to the expression
with the incomplete gamma function above.
>
Apparently via Gamma(-1,x)=Ei(-x)+e^(-x)/x+1/2 (log(-1/x)-log(-x))+log(x)
and the connection between Ei and Ci. But it does check out!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8624#comment:10>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
