Re: Simple but difficult integral ? Help ..!??

• To: mathgroup at smc.vnet.net
• Subject: [mg13920] Re: [mg13902] Simple but difficult integral ? Help ..!??
• From: BobHanlon at aol.com
• Date: Mon, 7 Sep 1998 01:22:45 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Dany,

Integrate[Sqrt[1 + Sin[x]^2], x]

EllipticE[x, -1]

This is the elliptical integral (EllipticE) of the second kind.  The x
in the output represents the unspecified upper limit of the implied
definite integral.

Integrate[Sqrt[1 + Sin[t]^2], {t, 0, x}]

EllipticE[x, -1]

If the upper limit is Pi/2 then this is the complete elliptic integral.

Integrate[Sqrt[1 + Sin[x]^2], {x, 0, Pi/2}]

EllipticE[-1]

More generally,

Integrate[Sqrt[1 - m Sin[t]^2], {t, 0, x}]

EllipticE[x, m]

Integrate[Sqrt[1 - m Sin[t]^2], {t, 0, Pi/2}]

EllipticE[m]

Bob Hanlon

In a message dated 9/6/98 7:34:38 AM, derijken at USA.net wrote:

>I need some help with the following intrgral
>
>Int ( sqrt ( 1 + (sin[x])^2  )) dx.

```

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