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MathGroup Archive 1998

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Re: Bivariate Integrations/Assumptions error/



I would like to point out that Integrate[ ] uses different algorithms
depending on whether it is definite or indefinite integration (Roach
1992, 'Indefinite and Definite Integration, Mathematica Conference
1992). Indefinite integration is centred about the Risch Structure
Theorem, definite integration involves contour integration. Therefore,
depending on how Integrate[ ] is used, we will obtain different
results. Paul Abbot in reply to [mg10603] noted that there was a
numerical argument in the expression being integrated, and numerical
evaluations are in this context not desired. Also note that changing
the limits of the definite integral from infinities to {x, x1, x2}, {y,
y1, y2}, results in an exact (and true) solution with no conditions.

Your integral may be fairly basic, but it illustrates a few aspects of
symbolic computation which need to be considered. I think you were
trying to check the answer given by Mathematica for a simple problem,
without realizing that the statement of the problem is not so easy to
formulate. There is, also, a necessity for Mathematica to consider by
default the arguments as broad as possible (i.e. Complex) because
otherwise the algorithms would be meaningless. With due care, a
symbolic engine like Mathematica can be very useful for the evaluation
of complicated expressions.





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