Open c22b6800-ec0b-4cbf-94c4-0a74aecc2093 opened 6 years ago
Description changed:
---
+++
@@ -1,7 +1,7 @@
Maxima interface returns a wrong result of this definite integral:
-sage: integrate(exp(t)sin(t),t,0,pi/2,algorithm='maxima')
+sage: integrate(exp(arccos(x)),x,0,1, algorithm='maxima')
-1/2e^(-1/2*pi) + 1/2
This is a Maxima problem because
(%i10) integrate(exp(acos(x)),x,0,1);
- %pi/2
1 %e
(%o10) - - ---------
2 2
Changed upstream from Not yet reported upstream; Will do shortly. to Reported upstream. No feedback yet.
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 ?
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
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
Maxima interface returns a wrong result of this definite integral:
while it should be:
This was reported in ask.sage: an integral with arccos wrong
Upstream: Reported upstream. No feedback yet.
Component: calculus
Keywords: integration, maxima
Issue created by migration from https://trac.sagemath.org/ticket/24008