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Mathematica gives bad integral ??
*To*: mathgroup at smc.vnet.net
*Subject*: [mg24293] Mathematica gives bad integral ??
*From*: "J.R. Chaffer" <jrchaff at mcn.net>
*Date*: Fri, 7 Jul 2000 00:11:33 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
Hi, this newbie gets erroneous results with Mathematica
4.0 (for students), with the following integral. Hopefully
someone can tell me why, and what I may be doing
wrong. I have tried "Assumptions -> x e Reals", or
x > 0, with same results. Integral in question is,
Integrate[1/Sqrt[1-Sin[2x]]]
The result is somewhat involved, instead of the expected
result (Schaum, "Calculus" 4E, p. 297),
integral = - (1/Sqrt[2])Log[Abs[Csc[Pi/4-x]-Cot[Pi/4-x]]]
One expects to get differing forms with any computer
algebra system, since there are so many equivalent forms
of algebraic expressions. However, Mathematica's form
and the Schaum (correct) form differ by significant
numerical values, as plotting shows (i.e., not some E-16
or some such).
Further, and what really seems wrong, is that when one
differentiates Mathematica's result for the integral, one
does NOT get the original integrand, or anything even
close, numerically.
So, I am confused. Anyone who knows the explanation
would be welcome to share it.
Thank you.
John Chaffer
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