MathGroup Archive 2000

[Date Index] [Thread Index] [Author Index]

Search the Archive

Mathematica gives bad integral ??


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




  • Prev by Date: Re: Division still cost more than multiplication?
  • Next by Date: Re: Division still cost more than multiplication?
  • Previous by thread: lancon
  • Next by thread: Re: Mathematica gives bad integral ??