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: |
Description (last modified by )
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
- Description modified (diff)
comment:2 Changed 4 years ago by
comment:3 Changed 4 years ago by
- 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
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
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
comment:6 Changed 4 weeks ago by
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
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This is a Maxima problem because