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