Dear list,
I have a few integrals cropping up where, no matter what questions you
ask, the answer is always the same. I realize that it's not possible
to have a complete decision tree or anything on these (especially with
the last one!), and perhaps some really can't be fixed, so I'm not
regarding them as bugs at this point.
However, any guidance on how to recognize in advance when they might
happen would be very appreciated. These are particularly strange
because the antiderivative Maxima gives, applied "naively" to the
endpoints, works fine in all three cases to get the answer Maxima
gives after all the questions, so in principle Maxima would give the
same answer just doing that, irrespective of having negative numbers
inside logs or square roots.
Thanks for any help!
#1
(%i10) integrate(1/sqrt(x-q), x, 1, 2);
Is q - 2 positive, negative, or zero?
zero;
#2
(%o10) 2 sqrt(2 - q) - 2 sqrt(1 - q)
(%i11) integrate(log(q-x), x, a, b);
Is b - a positive, negative, or zero?
positive;
(%o11) (b - q) log(q - b) - (a - q) log(q - a) - b + a
#3
(%i12) integrate(1/sqrt(q^2-x^2),x, a, b);
Is b - a positive, negative, or zero?
negative;
Is q - a positive, negative, or zero?
zero;
Is q + a positive, negative, or zero?
zero;
Is q + b positive, negative, or zero?
negative;
b a
(%o12) asin(------) - asin(------)
abs(q) abs(q)