Re: Wrong result of Integrate with assumptions -- my
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- Subject: [mg131612] Re: Wrong result of Integrate with assumptions -- my
- From: Alex Krasnov <akrasnov at cory.eecs.berkeley.edu>
- Date: Wed, 11 Sep 2013 03:51:33 -0400 (EDT)
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Consider the following simpler examples (Mathematica 8.0.4):
In: Expand[ExpToTrig[Integrate[t*E^(I*3*t), {t, a, b}] /. {a -> -1, b -> 2}]]
Out: (-1/9 - I/3)*Cos[3] + (1/9 - (2*I)/3)*Cos[6] - (1/3 - I/9)*Sin[3] + (2/3 + I/9)*Sin[6]
In: Expand[Assuming[Element[{a, b}, Reals], Integrate[t*E^(I*3*t), {t, a, b}]] /. {a -> -1, b -> 2}]
Out: (-1/9 + I/3)*Cos[3] + (1/9 - (2*I)/3)*Cos[6] - (1/3 + I/9)*Sin[3] + (2/3 + I/9)*Sin[6]
The second result is already incorrect.
Alex
On Mon, 9 Sep 2013, Youngjoo Chung wrote:
> Hi,
>
> Actually, none of the assumptions are necessary. Integrate returns the result in the form ConditionalExpresssion[...] in case certain conditions must be met for the result to be valid. Otherwise, it is not necessary to add the Assumptions option.
>
> Nevertheless, res2 is not always correct as you mentioned. After some arithmetic, I observed that Re[res2] is always correct but Im[res2] is correct only when a > 0 and b > 0 regardless of w assuming Abs[a] < Infinity and Abs[b] < Infinity.
>
> Sincerely,
> Youngjoo Chung
>
- References:
- Re: Wrong result of Integrate with assumptions -- my fault?
- From: Youngjoo Chung <ychung12@gmail.com>
- Re: Wrong result of Integrate with assumptions -- my fault?