#1594 integrate( cos(a)/ sqrt((tan(a))^2 + 1), a, -%pi/2, %pi/2 );

closed
nobody
5
2009-11-29
2009-02-17
No

Maxima can't caluculate definite integral
integrate( cos(a)/ sqrt((tan(a))^2 + 1), a, -%pi/2, %pi/2 );

It gives me
The number 1 isn't in the domain of atanh
-- an error. To debug this try debugmode(true);

If I calculate indefinite integral
integrate( cos(a)/ sqrt((tan(a))^2 + 1), a);
and manually put in integration limits, it gives the correct result %pi/2.

Discussion

  • Raymond Toy

    Raymond Toy - 2009-02-17

    FWIW, maxima is trying to find the roots of the denominator to see if there are any poles on the interval of integration. SOLVE is getting confused.

    A workaround would be to set intanalysis (undocumented) to false. Then integrate returns %pi/2.

     
  • Dieter Kaiser

    Dieter Kaiser - 2009-11-14
    • status: open --> pending
     
  • Dieter Kaiser

    Dieter Kaiser - 2009-11-14

    Documentation for intanalysis has been added to Integration.texi revision 1.45. The integral of this bug report has been added as an example.
    Maxima does not give a wrong result and is able to solve the integral with the help of the option variable intanalysis. More might be possible, but this would be a feature request.

    Setting the status to pending and the resolution to "Works for me".
    Dieter Kaiser

     
  • SourceForge Robot

    • status: pending --> closed
     
  • SourceForge Robot

    This Tracker item was closed automatically by the system. It was
    previously set to a Pending status, and the original submitter
    did not respond within 14 days (the time period specified by
    the administrator of this Tracker).

     

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