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Why does Mathematica give an incorrect answer to this multiple integral?

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  • Why does Mathematica give the wrong answer when integrating?

    I integrate Integrate[Exp[I Cos[b - c]] Cos[b], {b, 0, 2 Pi}] Mathematica gives: 2 I Pi BesselJ[1, 1] Which is indepedent on $c$. However, the result is NOT independent on $c$. The numerical value of what Mathematica gives is 0. + 2.76492 I while NIntegrate[Exp[I Cos[b - 0.5]] Cos[b], {b, 0, 2 Pi}] Gives 1.16655*10^-10 + 2.42645 I Certainly not the same. If we multiply the value Mathematica gives with $\cos(0.5)$ the result is the same. What is wrong?

    Answer:

    Looks like a bug that ran off in the development version of Mathematica. In[1]:= Integrate[Exp[I Cos...

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