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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?