Integration bug? Integrate[Sin[2 t]^2 Cos[Cos[t - p]], {t, 0, 2 Pi}]

*To*: mathgroup at smc.vnet.net*Subject*: [mg126248] Integration bug? Integrate[Sin[2 t]^2 Cos[Cos[t - p]], {t, 0, 2 Pi}]*From*: sykesy <sykesy at gmail.com>*Date*: Fri, 27 Apr 2012 06:47:49 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com

Hi all, I am trying to compute the following integral Integrate[Sin[2 t]^2 Cos[Cos[t - p]], {t, 0, 2 Pi}, Assumptions->p>0] for which Mathematica gives me the answer, 8 Pi (BesselJ[2,1]-BesselJ[3,1]) I was confused as to why the integral did not depend on p. I used the following numerical approach to the problem, Plot[NIntegrate[Sin[2 t]^2 Cos[Cos[t - p]], {t, 0, 2 Pi}], {p, 0, 2 Pi}] And found that the integral did depend on p. Is there something I am missing here? For a long time I thought I must be doing something very obvious wrong, but I can't see what it would be. Can anybody help me with this issue? best wishes, Andrew Sykes