Mathematica 11.1 Can someone explain why in the following “Assumptions” does not work as expected: Integrate[ Sin[n x]^2, {x, 0, 2 Pi}, Assumptions -> n \[Element] Integers] This gives: Pi - Sin[4 n Pi ]/(4 n) The second part is clearly redundant, but not even “Simplify” or “FullSimplify” will…

Dear Daniel, FullSimplify will eliminate it. But you have to tell it the assumptions again: FullSimplify[Integrate[Sin[n x]^2, {x, 0, 2 Pi}, Assumptions -> n[Element] Integers], Assumptions -> n \[Element] Integers] gives just Pi. Of course, one assumption in the outer most function does the tric…

The result is correct, because one needs to account for n = 0, for this case the integral is 0. (The limit of the Sin[4n\[Pi]]/(4*n) for n -> 0 is Pi, such that it is cancelled. I would say that it is perhaps a bug in FullSimplify. Though sometimes solutions are given that are true for most values.…

Dear Sander, I don’t think that this is a bug. In the documentation for FullSimplify under Possible Issues it says: Some of the transformations used by FullSimplify are only generically correct: I think that this is one of these cases. Cheers, Marco

Hi Sander, unfortunately the same “singularity” shows even when you exclude the case n = 0: Integrate[ Sin[n x]^2, {x, 0, 2 Pi}, Assumptions → n>0]

That was exactly my point; sometimes they simplify to things that are correct most of the time, like my example…

If you want to make a point you should include the other assumption as well: Integrate[Sin[n x]^2, {x, 0, 2 Pi}, Assumptions -> n > 0 \[And] n \[Element] Integers] And yes, I agree, for this case it could be more simplified. However, Integrate does not promise you to give the easiest possible outc…

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Use Assumptions and Integrate?

Questions

danl (Daniel Lichtblau) April 27, 2017, 10:34pm 8

Actually I have commented on various aspects in various forums. Here are some links.

https://mathematica.stackexchange.com/questions/67080/how-to-code-around-known-mma-special-case-failures

https://mathematica.stackexchange.com/questions/19833/usage-of-assuming-for-integration

https://mathematica.stackexchange.com/questions/51967/generate-conditions-seems-to-not-work

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Use Assumptions and Integrate?

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