Re: Problem with antiderivtive of ArcSec
- To: mathgroup at smc.vnet.net
- Subject: [mg24453] Re: Problem with antiderivtive of ArcSec
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Tue, 18 Jul 2000 00:58:56 -0400 (EDT)
- Organization: University of Western Australia
- References: <8k9j1o$fr1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <8k9j1o$fr1 at smc.vnet.net>, heathw at in-tch.com wrote:
> I am trying to integrate the following function:
> 1/(x*Sqrt[x^2-1])
> The solution should be simply:
> ArcSec[x]
> Mathmatica gives:
> -ArcTan[1/Sqrt[x^2-1]]
And the two answers differ by a constant. Here is one way to get the
textbook answer:
Notebook[{
Cell[CellGroupData[{
Cell[BoxData[
\(TraditionalForm\`\[Integral]\_1\%y\(
1\/\(x\ \ at \(x\^2 - 1\)\)\) \[DifferentialD]x\)], "Input"],
Cell[BoxData[
\(TraditionalForm\`If[y > 1,
1\/2\ \((\[Pi] -
2\ \(\(sin\^\(-1\)\)(1\/y)\))\), \[Integral]\_1\%y\(
1\/\(x\ \ at \(x\^2 - 1\)\)\) \[DifferentialD]x]\)], "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
\(TraditionalForm\`FullSimplify[%, y > 1]\)], "Input"],
Cell[BoxData[
\(TraditionalForm\`\(sec\^\(-1\)\)(y)\)], "Output"]
}, Open ]]
}
]
Cheers,
Paul
--
Paul Abbott Phone: +61-8-9380-2734
Department of Physics Fax: +61-8-9380-1014
The University of Western Australia
Nedlands WA 6907
AUSTRALIA http://physics.uwa.edu.au/~paul