Am I missing something in this integral?

Question

I am trying to solve this simple integral:

Integrate[Cos[m*x]*Cos[mp*x], {x, 0, 2 \[Pi]}, 
 Assumptions ->  
  Element[m - mp, Integers] && Element[m + mp, Integers] && 
   m - mp != 0 && m + mp != 0]

which is zero. However, Mathematica gives:

1/2 (Sin[2 (m - mp) \[Pi]]/(m - mp) + Sin[2 (m + mp) \[Pi]]/(m + mp))

Why?, any tip?

Thanks

The result is correct, to see it is just 0 you need Simplify[%, (m | mp) ∈ Integers], or Assuming or $Assumptions etc. Take a look at closely related post: How to specify assumptions before evaluation? — Artes, Oct 06 '13 at 13:22

score 2 · Accepted Answer · answered Oct 06 '13 at 11:20

2

Assuming[(Element[m - mp, Integers] && Element[m + mp, Integers] && 
   m - mp != 0 && m + mp != 0), 
 Integrate[Cos[m*x]*Cos[mp*x], {x, 0, 2 \[Pi]}]]

yields 0. It seems that functions of the parameters in assumptions are not interpreted,

answered Oct 06 '13 at 11:20

ubpdqn

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Am I missing something in this integral?

1 Answers1