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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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