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## maxima-bugs

 [Maxima-bugs] [ maxima-Bugs-991628 ] integrate(x^n,x,a,b) wrong for a<0 - 2004-07-15 14:45:19 ```Bugs item #991628, was opened at 2004-07-15 10:45 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 Category: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x^n,x,a,b) wrong for a<0 b^(n+1)/(n+1)-a^(n+1)/(n+1) (NO!) This is incorrect for (e.g.) n=-2, a<0 Integral is divergent (OK) Same thing, but a more dramatic demo: assume(equal(a,-1),equal(b,1),equal(n,-2)); integrate(x^n,x,a,b) => b^(n+1)/(n+1)-a^(n+1)/(n+1) (NO!) vs. integrate(x^-2,x,-1,1) => Divergent (OK) Also assume(equal(n,-2)); integrate(x^n,x,-1,1); => (-1)^n/(n+1)+1/(n+1) (NO!) ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-991628 ] integrate(x^n,x,a,b) wrong for a<0 - 2006-04-10 04:09:11 ```Bugs item #991628, was opened at 2004-07-15 08:45 Message generated for change (Settings changed) made by robert_dodier You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. >Category: Lisp Core - Integration Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x^n,x,a,b) wrong for a<0 b^(n+1)/(n+1)-a^(n+1)/(n+1) (NO!) This is incorrect for (e.g.) n=-2, a<0 Integral is divergent (OK) Same thing, but a more dramatic demo: assume(equal(a,-1),equal(b,1),equal(n,-2)); integrate(x^n,x,a,b) => b^(n+1)/(n+1)-a^(n+1)/(n+1) (NO!) vs. integrate(x^-2,x,-1,1) => Divergent (OK) Also assume(equal(n,-2)); integrate(x^n,x,-1,1); => (-1)^n/(n+1)+1/(n+1) (NO!) ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-991628 ] integrate(x^n,x,a,b) wrong for a<0 - 2006-04-10 17:33:09 ```Bugs item #991628, was opened at 2004-07-15 10:45 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Lisp Core - Integration Group: None Status: Open Resolution: None Priority: 5 Submitted By: Stavros Macrakis (macrakis) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x^n,x,a,b) wrong for a<0 b^(n+1)/(n+1)-a^(n+1)/(n+1) (NO!) This is incorrect for (e.g.) n=-2, a<0 Integral is divergent (OK) Same thing, but a more dramatic demo: assume(equal(a,-1),equal(b,1),equal(n,-2)); integrate(x^n,x,a,b) => b^(n+1)/(n+1)-a^(n+1)/(n+1) (NO!) vs. integrate(x^-2,x,-1,1) => Divergent (OK) Also assume(equal(n,-2)); integrate(x^n,x,-1,1); => (-1)^n/(n+1)+1/(n+1) (NO!) ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2006-04-10 13:33 Message: Logged In: YES user_id=28849 These errors occur because maxima is trying to see if there are any poles on the real axis. It does so by calling poles-in-interval, which calls real-roots on the denominator of the integrand, which is x^(-n), since n is negative. But solve thinks this equation has no real roots. This is why x^(-2) works. solve wants the roots of x^2, which it can figure out, and thus poles-in-interval finds poles in the interval. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=991628&group_id=4933 ```