Integrate this how?

*To*: mathgroup at smc.vnet.net*Subject*: [mg116294] Integrate this how?*From*: BoLe <bole79 at gmail.com>*Date*: Thu, 10 Feb 2011 05:21:36 -0500 (EST)

Curve is closed (t from -Pi to Pi) and in polar form r[t_]:=(1+Sin[t]) (1+9/10 Cos[8 t]) (1+1/10 Cos[24 t]) (9/10+5/100 Cos[200 t]) Would like to find out its arc length, so the integral of Sqrt[r[t]^2+D[r[t],t]^2] Version 7 complains but returns a somewhat reasonable number (something around 50; drew together with a circle of the same length), version 8 says nothing but gives just too low a number (five and something). How can this be? New Mathematica should have no problem with such high oscillatory integrands, shouldn't she?