Re: A problem definite integral from the past

mecej4 <mecej4@xxxxxxxxxxxxx> writes:

About a decade ago, Maple 5.3 and 5.4 could not calculate the definite
integral

evalf(int((x/sin(x))^(1/3),x=0..Pi);

(several minutes of running on a 486 CPU with no answer, if I remember
correctly) whereas Mathematica 3 and 4 had no such difficulty (< 2
seconds on the same 486). On one or two occasions, I went into a
Maplesoft booth at some technical conferences and let them apply their
software on this problem.

The integral has two singularities (at 0 and Pi); the first one is
trivial to handle, but the second needs a little more effort. The
integral arises in the theory of condensation of a vapor on a horizontal
cylinder.

I'd appreciate if people with access to more recent versions of Maple
would try this out -- I'd like to find out the earliest version that can
treat this problem (if such a version exists).

Maple 7, I think.

I am also curious about why Maple 5.x failed.

Somehow the combination of the two singularities seems to have given it
trouble. It had no problem with doing the integral on 0..Pi/2 or Pi/2 .. Pi.
--
Robert Israel israel@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada
.

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