Re: RE: Bug in math4

• To: mathgroup at smc.vnet.net
• Subject: [mg20703] Re: [mg20662] RE: [mg20633] Bug in math4
• From: BobHanlon at aol.com
• Date: Mon, 8 Nov 1999 02:48:46 -0500
• Sender: owner-wri-mathgroup at wolfram.com

```Ted,

Re: Integrate[Sqrt[2-Sin[x]],{x,1,Pi/2,4}]

I cannot find any documentation in the on-line Help nor at
http://www.dot.net.au/~elisha/ersek/Tricks.html for use of the additional
(third of four) argument in the iterator in Integrate (Pi/2 in this case).

What is this argument doing and where is its use documented?

Thanks,

Bob Hanlon

In a message dated 11/7/1999 6:22:40 AM, ErsekTR at navair.navy.mil writes:

>Lennart Bengtsson indicated the problem discussed earlier might be at
>x=Pi/2.  Below we see this is the case. I don't know I didn't make the
>connection between 1.57... and Pi/2 earlier.
>
>
>In[1]:=
>Integrate[Sqrt[2-Sin[x]],{x,1,4}]
>
>Out[1]=  (*** Wrong answer ***)
>-2*EllipticE[(-4 + Pi/2)/2, -2] +
> 2*EllipticE[(-1 + Pi/2)/2, -2] +
> 4*EllipticF[I*ArcSinh[1/Sqrt[2]], -2]
>
>
>In[2]:=
>Integrate[Sqrt[2-Sin[x]],{x,1,Pi/2,4}]
>
>Out[2]=   (*** Right answer ***)
>-2*EllipticE[(-4 + Pi/2)/2, -2] +
>2*EllipticE[(-1 + Pi/2)/2, -2]
>

```

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