Re: Wrong result of Integrate with assumptions -- my

*To*: mathgroup at smc.vnet.net*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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <ks82sr$jnp$1@smc.vnet.net> <20130909040629.D3B716A22@smc.vnet.net>

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>