[Maxima-bugs] [ maxima-Bugs-991628 ] integrate(x^n,x,a,b) wrong for a<0<b

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Bugs item #991628, was opened at 2004-07-15 10:45
Message generated for change (Comment added) made by rtoy
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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

Initial Comment:
integrate(x^n,x,a,b);
Is  n  positive, negative, or zero? neg;
Is  n + 1  zero or nonzero? n;
Is  b - a  positive, negative, or zero? pos;
  => b^(n+1)/(n+1)-a^(n+1)/(n+1)  (NO!)

This is incorrect for (e.g.) n=-2, a<0<b:

integrate(x^-2,x,a,1);
Is  a - 1  positive, negative, or zero?  neg;
  => 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!)



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>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.

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