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.