Opened 4 years ago

Last modified 4 weeks ago

#24008 new defect

exponential integral of arccos

Reported by: mforets Owned by:
Priority: major Milestone: sage-8.1
Component: calculus Keywords: integration, maxima
Cc: Merged in:
Authors: Reviewers:
Report Upstream: Reported upstream. No feedback yet. Work issues:
Branch: Commit:
Dependencies: Stopgaps:

Status badges

Description (last modified by mforets)

Maxima interface returns a wrong result of this definite integral:

sage: integrate(exp(arccos(x)),x,0,1, algorithm='maxima')                         
-1/2*e^(-1/2*pi) + 1/2

while it should be:

sage: integrate(exp(arccos(x)),x,0,1, algorithm='sympy')
1/2*e^(1/2*pi) + 1/2

This was reported in ask.sage: an integral with arccos wrong

Change History (6)

comment:1 Changed 4 years ago by mforets

  • Description modified (diff)

comment:2 Changed 4 years ago by rws

This is a Maxima problem because

(%i10) integrate(exp(acos(x)),x,0,1);
                                       - %pi/2
                                 1   %e
(%o10)                           - - ---------
                                 2       2

comment:3 Changed 4 years ago by mforets

  • Report Upstream changed from Not yet reported upstream; Will do shortly. to Reported upstream. No feedback yet.

Ok, thank you!

i've sent an upstream report

comment:4 Changed 4 weeks ago by chapoton

There is something strange going on:

maxima: f:exp(acos(x));                                                         
%e^acos(x)
maxima: integrate(f,x,0,1);                                                     
1/2-%e^-(%pi/2)/2
maxima: integrate(1/f,x,0,1);                                                   
1/2-%e^-(%pi/2)/2

How would one try to debug that ?

comment:5 Changed 4 weeks ago by chapoton

The problem is also there (after change of variable) in

(%i8) integrate(exp(acos(cos(y)))*sin(y),y,0,%pi/2);
                                       - %pi/2
                                 1   %e
(%o8)                            - - ---------
                                 2       2
(%i9) integrate(exp(y)*sin(y),y,0,%pi/2);
                                    %pi/2
                                  %e        1
(%o9)                             ------- + -
                                     2      2

(%i12) integrate(exp(-y)*sin(y),y,0,%pi/2);
                                       - %pi/2
                                 1   %e
(%o12)                           - - ---------
                                 2       2
Last edited 4 weeks ago by chapoton (previous) (diff)

comment:6 Changed 4 weeks ago by chapoton

so this depends on the allowed trig simplifications:

(%i50) triginverses:all;
(%o50)                                all
(%i51) integrate(exp(acos(cos(y)))*sin(y),y,0,%pi/2);
                                    %pi/2
                                  %e        1
(%o51)                            ------- + -
                                     2      2
(%i52) triginverses:true;   
(%o52)                               true
(%i53) integrate(exp(acos(cos(y)))*sin(y),y,0,%pi/2);
                                       - %pi/2
                                 1   %e
(%o53)                           - - ---------
                                 2       2
Last edited 4 weeks ago by chapoton (previous) (diff)
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