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MathGroup Archive 2002

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RE: Why can't Mathematica do this simple integral ?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36895] RE: Why can't Mathematica do this simple integral ?
  • From: Madhusudan Singh <spammers-go-here at yahoo.com>
  • Date: Tue, 1 Oct 2002 04:45:26 -0400 (EDT)
  • References: <an14h9$ie2$1@smc.vnet.net>
  • Reply-to: spammers-go-here at yahoo.com
  • Sender: owner-wri-mathgroup at wolfram.com

On Friday 27 September 2002 04:18 am, DrBob, as drbob at bigfoot.com, held forth the 
following in comp.soft-sys.math.mathematica (<an14h9$ie2$1 at smc.vnet.net>) :

> You would need to make assumptions about y, and you can't.  The function
> and the limits have to take care of that, and when you try to do that,
> you end up with an expression that has different antiderivatives on
> different regions, for different values of x.  So, you have to break it
> up.  The assumption x > 0 implies that x is real, so Im[x]==0 is
> unnecessary.
> 
> one = Integrate[Cosh[2 (y - x)]
>       2 y, {y, Min[x, 1/2], 1/2}, Assumptions -> {x > 0}];
> two = Integrate[Cosh[2 (x - y)] 2
>       y, {y, 0, Min[x, 1/2]}, Assumptions -> {x > 0}];
> one + two // FullSimplify
> Plot[{one, two, one + two}, {x, 0, 1/2}];
> 
>  (1/4)*E^(-1 - 2*x)*(E + (-2 + E)*E^(4*x))
> 
> Bobby Treat
> 
> -----Original Message-----
> From: Madhusudan Singh [mailto:spammers-go-here at yahoo.com]
To: mathgroup at smc.vnet.net
> Subject: [mg36895]  Why can't Mathematica do this simple integral ?
> 
> Hi
>         I have been trying to integrate the following :
> 
>         Integrate[Cosh[2 Abs[x-y]] 2 y, {y,0,1/2},
>   Assumptions->{Im[x]==0,x>0}]
> 
>         However, Mathematica chokes and simply returns the integral as
> it is. However, if I
>  split up the integral into two portions, it quickly gives me an answer
> for the parts. Is
>  there something implicit that I am missing in the Assumptions ?
> 
> Thanks,
> 
> MS.
> 


Thanks for your response. But why can't Mathematica give the answer in the If[x.....] form 
?

Anyways, I will try what you suggest.

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