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


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



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